Methods of modular construction of 0d-state tunnel junction devices and methods of use thereof

Abstract

Disclosed herein are methods of modular construction of 0D-state tunnel junction devices and methods of use thereof.

Description

[0001] METHODS OF MODULAR CONSTRUCTION OF OD-STATE TUNNEL

[0002] JUNCTION DEVICES AND METHODS OF USE THEREOF

[0003] CROSS-REFERENCE TO RELATED APPLICATIONS

[0004] This application claims the benefit of priority to U.S. Provisional Application No. 63 / 605,730 filed December 4, 2023, which is hereby incorporated herein by reference in its entirety.

[0005] STATEMENT OF GOVERNMENT SUPPORT

[0006] This invention was made with government support under grant / contract number 1936219 awarded by the National Science Foundation. The government has certain rights in the invention.

[0007] BACKGROUND

[0008] Electronic spectroscopy of zero-dimensional (0D) quantum systems is an important tool for developing a fundamental understanding of these systems. Toward this end, scanning tunneling spectroscopy (STS) has demonstrated atomic-scale sensitivity, but is not easily scalable for applications, whereas device-based approaches rely on embedding these systems within a solid-state tunnel junction (TJ) and are not generally applicable.

[0009] Compositions and devices with improved properties are needed. For example, compositions, methods, and devices for improved study of 0D quantum systems are needed. The compositions, methods, and devices discussed herein addresses these and other needs.

[0010] SUMMARY

[0011] In accordance with the purposes of the disclosed compositions, methods, and devices as embodied and broadly described herein, the disclosed subject matter relates to methods of modular construction of OD-state tunnel junction devices and methods of use thereof.

[0012] For example, described herein is a modular design for a 0-D state tunnel junction device comprising: a first conductive layer; a first insulating layer disposed on and in electrical and physical contact with at least a portion of the first conductive layer, the first insulating layer comprising a first two-dimensional material; a second insulating layer disposed on and in electrical and physical contact with at least a portion of the first insulating layer, such that at least a portion of the first insulating layer is sandwiched between at least a portion of the second insulating layer and at least a portion of the first conductive layer, the second insulating layer comprising a second two-dimensional (2D) material; an impurity sandwiched between and substantially encapsulated by the first insulating layer and the second insulating layer, the impurity being in electrical and physical contact with at least a portion of both the first insulating layer and the second insulating layer, the impurity comprising a defect, an atom, a molecule, or a combination thereof, wherein the impurity is a zero-dimensional (OD) system; and a second conductive layer disposed on and in electrical and physical contact with at least a portion of the second insulating layer, such that at least a portion of the second insulating layer is sandwiched between at least a portion of the first insulating layer and at least a portion of the first conductive layer.

[0013] In some examples, the first conductive layer comprises a two-dimensional material.

[0014] In some examples, the second conductive layer comprises a two-dimensional material.

[0015] In some examples, the first conductive layer comprises graphene, such as monolayer graphene or multi-layered graphene.

[0016] In some examples, the second conductive layer comprises graphene, such as monolayer graphene or multi-layered graphene.

[0017] In some examples, the first conductive layer and the second conductive layer are substantially the same.

[0018] In some examples, the first conductive layer and the second conductive layer are different.

[0019] In some examples, the first insulating layer comprises hexagonal boron nitride, such as monolayer hexagonal boron nitride or multi-layered hexagonal boron nitride.

[0020] In some examples, the second insulating layer comprises hexagonal boron nitride, such as monolayer hexagonal boron nitride or multi-layered hexagonal boron nitride.

[0021] In some examples, the first insulating layer has an average thickness of from 1 nanometer to 5 nanometers, such as from 1.5 to 3.5 mm or from 1 to 3 nm.

[0022] In some examples, the second insulating layer has an average thickness of from 1 nanometer to 5 nanometers, such as from 1.5 to 3.5 mm or from 1 to 3 nm.

[0023] In some examples, the first insulating layer and the second insulating layer are substantially the same.

[0024] In some examples, the first insulating layer and the second insulating layer are different.

[0025] In some examples, the first insulating layer and the second insulating layer together have a total average thickness of from 2 to 10 nanometers, such as from 3 to 7 nm or from 4 to 6 nanometers.

[0026] In some examples, the impurity comprises a defect, such as a vacancy, an interstitial defect, a dopant, or a combination thereof.

[0027] In some examples, the impurity comprises a metal atom, such as a metal selected from the group consisting of Er, Mn, Pt, Fe, V, Cu, Co, Yb, Pr, Eu, and combinations thereof.

[0028] In some examples, the impurity comprises a molecule, such as a macrocyclic ligand. In some examples, the impurity comprises a molecule, such as a porphyrin, a corrole, a phthalocyanine, or a combination thereof.

[0029] In some examples, the molecule comprises a metal-ligand molecule, such as a metal porphyrin, a metal corrole, a metal phthalocyanine, or a combination thereof. In some examples, the metal comprises Cu, V, Co, Fe, Mn, Zn, Ni, Cr, Ti, or a combination thereof.

[0030] In some examples, the impurity comprises a molecule, such as copper phthalocyanine, vandyl phthalocyanine, or a combination thereof.

[0031] In some examples, the impurity comprises a molecule, such as one or more of those shown in Figure 4.

[0032] In some examples, the impurity comprises a third two-dimensional material, optionally further comprising a defect therein.

[0033] In some examples, the device further comprises a first electrode disposed on and in electrical and physical contact with at least a portion of the first conductive layer. In some examples, the first electrode comprises a metal, such as gold, and / or a magnetic material.

[0034] In some examples, the device further comprises a second electrode disposed on and in electrical and physical contact with at least a portion of the second conductive layer. In some examples, the second electrode comprises a metal, such as gold, and / or a magnetic material.

[0035] In some examples, the tunnel junction device is a qubit.

[0036] Also disclosed herein are methods of making any of the devices described herein. In some examples, the method comprises, in any order: disposing the first insulating layer on at least a portion of the first conductive layer; disposing the impurity on the first insulating layer or the second insulating layer; disposing at least a portion of the first insulating layer on at least a portion of the second insulating layer to substantially encapsulate the impurity; disposing the second insulating layer on at least a portion of the first insulating layer; and disposing the second conductive layer on at least a portion of the second insulating layer. In some examples, disposing the first conductive layer, the first insulating layer, the second insulating layer, the second conductive layer, or a combination thereof comprises mechanical exfoliation and / or dry transfer. In some examples, disposing the impurity comprises drop casting, spin casting, evaporation, or a combination thereof.

[0037] Also disclosed herein are articles of manufacture comprising any of the devices disclosed herein. In some examples, the article comprises a quantum device, such as a quantum information system, a quantum computing device, a quantum sensor, a quantum transduction device, or a combination thereof.

[0038] Also disclosed herein are methods of use of any of the devices disclosed herein. In some examples, the method comprises using the device in a quantum device, such as a quantum information system, a quantum computing device, a quantum sensor, a quantum transduction device, or a combination thereof.

[0039] In some examples, the method comprises using the device to characterize the impurity. In some examples, the method comprises using ESR (e.g., pulsed ESR) to characterize the impurity.

[0040] Additional advantages of the disclosed compositions, devices, and methods will be set forth in part in the description which follows, and in part will be obvious from the description. The advantages of the disclosed compositions, devices, and methods will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosed devices and methods, as claimed.

[0041] The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.

[0042] BRIEF DESCRIPTION OF THE FIGURES

[0043] The accompanying figures, which are incorporated in and constitute a part of this specification, illustrate several aspects of the disclosure, and together with the description, serve to explain the principles of the disclosure.

[0044] Figure 1. (Top Panel) IV and dl / dV acquired from a graphene / hBN / VOPc / hBN / graphene tunnel junction. Peaks in dl / dV correspond to steps in IV as resonant tunneling through VOPc molecular orbitals is allowed. (Middle Panel) Same dl / dV data from Top Panel, but with the direct tunneling background removed by fitting to a polynomial background. There is a clear resonance at -2.1 V representing the VOPc HOMO, and additional structure at positive bias that may correspond to the VOPc LUMO. (Bottom Panel) STM based tunneling spectra of a similar structure (graphite / hBN / VOPc) confirming the HOMO and LUMO energies of the VOPc.

[0045] Figure 2. Encapsulation process. An initial stack of graphene / hBN is created by mechanical exfoliation and transfer. Molecular qubits are deposited, then another h-BN flake and the top graphene electrode are deposited via mechanical transfer. The full graphene / hBN / molecule / hBN / graphene stack is then contacted with metal electrodes, for example using standard lithography techniques. Final image is a cross-sectional view of the fully assembled device. Figure 3. Tunable molecular qubits. By modulating the distance of nuclear spin bearing atoms, coherence time is changed, and the potential for coherence transfer is also created (Zadrozny JM et al. (2015) Millisecond Coherence Time in a Tunable Molecular Electronic Spin Qubit. ACS Central Science, l(9):488-492).

[0046] Figure 4. Sample compounds amenable to functionalization and deposition via ultrahigh vacuum techniques. Each site (Xa-d) is separately functionalizable synthetically, providing a large array of possibilities for tuning the ligand field parameters. Each of these compounds can also undergo axial coordination, providing another axis along which to modify the electronic properties.

[0047] Figure 5. STM image of a layer of VOPc molecules deposited onto a half-device structure (e.g., graphene / hBN / VOPc). Image shows the ordering within the molecular layer, with dotted circles highlighting a molecular vacancy (dark feature) and an additional VOPc on top of the layer (bright feature).

[0048] Figure 6A-Figure 6C. Electrical characterization of a hBN tunnel junction (hBN-TJ) device. Figure 6A, Schematic of the hBN-TJ device structure. The 2D heterostructure features multi-layer graphene (MLG) contacts to a hBN barrier layer. Figure 6B, Optical image of a hBN-TJ device. Figure 6C, I-V, black curve, and dl / dV, purple curve, at room temperature. Plateaus in I-V and broad peaks in dl / dV are due to the resonant tunneling caused by native defect states in the hBN barrier. Inset, a schematic of the energy diagram of the TJ device. Discrete lines represent the energy states of the native defects within the hBN bandgap.

[0049] Figure 7A-Figure 7B. Tunneling spectroscopy of quantum point defects in hBN. Figure 7 A, dl / dV of the hBN tunnel junction (hBN-TJ) devices at 15 K for three sources of pure hBN: commercial hBN from HQ Graphene, Ames hBN, and MANA hBN. Tunneling spectrum of the MANA hBN device reveals no significant resonant tunneling peaks (Figure 11). Figure 7B, dl / dV of carbon-related defects in Ames hBN at 15 K. Inset, a zoomed in dl / dV around -I V, indicating the sharpness of the atomic-like resonant peaks.

[0050] Figure 8A-Figure 8E. STM of molecular qubits: VOPc on hBN. Figure 8A, Structure of VOPc molecule. Figure 8B, A schematic of the STM setup containing a ‘half tunnel junction’ device as studied by STM and STS Figure 8C, STM topographic image of a bilayer of VOPc deposited on a monolayer hBN on an HOPG substrate (STM imaging conditions: +2.3 V, 326 pA). Figure 8D, dl / dV of VOPc at 5 K measured by an STM setup with tip located at the molecule center (top curve) or molecule lobe (bottom curve). Figure 8E, dl / dV of VOPc encapsulated in 2D-TJ device at 15 K (green curve). The dashed black curved is direct tunneling model. Top inset, a schematic of the VOPc-TJ device with heterostructure of MLG / hBN / VOPc / hBN / MLG. Bottom inset, a schematic of the energy diagram of the device with discrete lines representing molecular states of VOPc

[0051] Figure 9. Comparison between spatially-averaged STS and VOPc devices. The green curve shows the experimental dl / dV (green curve in Figure 8E) subtracted from direct tunneling model for a VOPc-TJ device (i.e., black curve in Figure 8E). The black curve is the calculated resonant dl / dV, and the wine curve represent the average of dl / dV scans as measured by STS on a VOPc bilayer film on hBN. STS were taken at 21 different tip locations and were normalized before averaging.

[0052] Figure lOA-Figure 10B. AFM image and the dependency of tunneling spectroscopy on hBN thickness. Figure 10A, An AFM scan image of the three-layer stack (MLG / hBN / MLG) for the device, with the corresponding optical image shown in Figure 6B. Figure 10B, dl / dV measurements for three hBN-TJ devices with various commercial hBN flack thicknesses: 2.4, 2.7 and 4.7 nm. The data reveal that increasing the hBN thickness led to a decrease in direct tunneling and resonance peaks become broader with less sharp resonance features.

[0053] Figure 11. Significant suppression of resonance tunneling in MANA hBN. Zooming in on the dl / dV data in Figure 7A (green curve) shows only a small and broad resonant tunneling peak around -0.25 V for the MANA hBN-TJ device.

[0054] Figure 12A-Figure 12C. Temperature dependency of tunneling spectroscopy for a C- doped hBN tunnel junction device. Figure 12A, dl / dV spectra at various temperatures: 15 K, 80 K, 100 K, 150 K, and 290 K. The data reveals that the resonant tunneling becomes broader as the temperature increases, and above 80 K, the line-shapes become distorted. Figure 12B, Lineshape analysis of the sharp resonant peak at -0.94 V. The line-shapes are fitted with linear (to remove the baseline) and Lorentzian functions and normalized by its maximum for temperatures ranging from 15 K up to 80 K. The blue lines are the fit results. Figure 12C, The full width at half maximum (FWHM) of the line-shape fitted results as a function of the temperature. The blue line is a linear fit to the data, indicating the line- shape increases linearly by increasing the temperature up to 80 K. Above 80 K, the line-shapes are distorted and cannot be fitted.

[0055] Figure 13A-Figure 13C. Sources of spatial variation in tunneling spectroscopy of VOPc on a hBN / HOPG half device. Figure 13 A, STM wide-area topographic image of a bare monolayer hBN on HOPG with atomic resolution and defects. Top inset, 2D-FFT of image, bottom inset, close-up of a single-point defect. Figure 13B, Another STM topographic image of a bare monolayer hBN on HOPG. There is a moire pattern (period ~14 nm) due to the lattice mismatch of the hBN and the HOPG. Inset, hBN atomic resolution. Figure 13C, Constantcurrent dl / dV map of VOPc bilayer on hBN / HOPG acquired simultaneously with topographic image in Figure 8C. Long distance fluctuations in contrast may reflect defects or the moire lattice in the underlying hBN. STM imaging conditions: Figure 13 A, (+2.6V, 78pA); Figure 13B, (+2.37V, 20pA) inset, (+620mV, 190pA); and Figure 13C, (+2.3V, 326pA).

[0056] Figure 14A-Figure 14C. Direct tunneling model, dashed curves are calculated direct tunneling at T= 15 K for various hBN-TJ device: Figure 14A, commercial hBN, Figure 14B, Ames hBN, and Figure 14C, MANA hBN.

[0057] Figure 15. powder X-ray diffraction (PXRD) patterns for VOPc, simulated (black) vs. experimental (purple) data were collected at room temperature using CuKal radiation ( = 1.5406 A). Simulation of PXRD pattern was based on single crystal X-ray diffraction data of VOPc as reported in Reference S2.

[0058] DETAILED DESCRIPTION

[0059] The compositions, methods, and devices described herein may be understood more readily by reference to the following detailed description of specific aspects of the disclosed subject matter and the Examples included therein.

[0060] Before the present compositions, methods, and devices are disclosed and described, it is to be understood that the aspects described below are not limited to specific synthetic methods or specific reagents, as such may, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular aspects only and is not intended to be limiting.

[0061] Also, throughout this specification, various publications are referenced. The disclosures of these publications in their entireties are hereby incorporated by reference into this application in order to more fully describe the state of the art to which the disclosed matter pertains. The references disclosed are also individually and specifically incorporated by reference herein for the material contained in them that is discussed in the sentence in which the reference is relied upon.

[0062] In this specification and in the claims that follow, reference will be made to a number of terms, which shall be defined to have the following meanings.

[0063] Throughout the description and claims of this specification the word “comprise” and other forms of the word, such as “comprising” and “comprises,” means including but not limited to, and is not intended to exclude, for example, other additives, components, integers, or steps.

[0064] As used in the description and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a composition” includes mixtures of two or more such compositions, reference to “an agent” includes mixtures of two or more such agents, reference to “the component” includes mixtures of two or more such components, and the like.

[0065] “Optional” or “optionally” means that the subsequently described event or circumstance can or cannot occur, and that the description includes instances where the event or circumstance occurs and instances where it does not.

[0066] Ranges can be expressed herein as from “about” one particular value, and / or to “about” another particular value. By “about” is meant within 5% of the value, e.g., within 4, 3, 2, or 1% of the value. When such a range is expressed, another aspect includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another aspect. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[0067] Values can be expressed herein as an “average” value. “Average” generally refers to the statistical mean value.

[0068] By “substantially” is meant within 5%, e.g., within 4%, 3%, 2%, or 1%.

[0069] “Exemplary” means “an example of’ and is not intended to convey an indication of a preferred or ideal embodiment. “Such as” is not used in a restrictive sense, but for explanatory purposes.

[0070] It is understood that throughout this specification the identifiers “first” and “second” are used solely to aid in distinguishing the various components and steps of the disclosed subject matter. The identifiers “first” and “second” are not intended to imply any particular order, amount, preference, or importance to the components or steps modified by these terms.

[0071] References in the specification and concluding claims to parts by weight of a particular element or component in a composition denotes the weight relationship between the element or component and any other elements or components in the composition or article for which a part by weight is expressed. Thus, in a compound containing 2 parts by weight of component X and 5 parts by weight component Y, X and Y are present at a weight ratio of 2:5, and are present in such ratio regardless of whether additional components are contained in the compound.

[0072] A weight percent (wt. %) of a component, unless specifically stated to the contrary, is based on the total weight of the formulation or composition in which the component is included.

[0073] The term “or combinations thereof’ as used herein refers to all permutations and combinations of the listed items preceding the term. For example, “A, B, C, or combinations thereof’ is intended to include at least one of: A, B, C, AB, AC, BC, or ABC, and if order is important in a particular context, also BA, CA, CB, CBA, BCA, ACB, BAC, or CAB. Continuing with this example, expressly included are combinations that contain repeats of one or more item or term, such as BB, AAA, AB, BBC, AAABCCCC, CBBAAA, CAB ABB, and so forth. The skilled artisan will understand that typically there is no limit on the number of items or terms in any combination, unless otherwise apparent from the context.

[0074] Modular OD-State Tunnel Junction Devices

[0075] Described herein are tunnel junction devices comprising a first conductive layer. The devices further comprise a first insulating layer disposed on and in electrical and physical contact with at least a portion of the first conductive layer, the first insulating layer comprising a first two-dimensional (2D) material. The devices further comprise a second insulating layer disposed on and in electrical and physical contact with at least a portion of the first insulating layer, such that at least a portion of the first insulating layer is sandwiched between at least a portion of the second insulating layer and at least a portion of the first conductive layer, the second insulating layer comprising a second two-dimensional material. The devices further comprise an impurity sandwiched between and substantially encapsulated by the first insulating layer and the second insulating layer, the impurity being in electrical and physical contact with at least a portion of both the first insulating layer and the second insulating layer, the impurity comprising a defect, an atom, a molecule, or a combination thereof, wherein the impurity is a zero-dimensional (OD) system. The devices further comprise a second conductive layer disposed on and in electrical and physical contact with at least a portion of the second insulating layer, such that at least a portion of the second insulating layer is sandwiched between at least a portion of the first insulating layer and at least a portion of the first conductive layer.

[0076] The first conductive layer and the second conductive layer can each independently comprise any suitable material. The first conductive layer and / or the second conductive layer can, for example, comprise(s) a transparent conducting oxide, a metal oxide, a conducting polymer, a carbon material, a metal, a magnetic conductor, or a combination thereof. The metal can comprise, for example, a metal selected from the group consisting of Be, Mg, Al, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Ba, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and combinations thereof. In some examples, the metal can comprise an alloy. Examples of conducting polymers include, but are not limited to, polyacetylene, polyalanine, poly(3,4- ethylenedi oxy thiophene) polystyrene sulfonate (“PEDOT-PSS”), and combinations thereof. Examples of carbon materials include, but are not limited to, graphitic carbon and graphites, including pyrolytic graphite (e.g., highly ordered pyrolytic graphite (HOPG)) and isotropic graphite, amorphous carbon activated carbon, hard carbon, carbon black, carbon fiber, single- or multi-walled carbon nanotubes, graphene, glassy carbon, diamond-like carbon (DLC) or doped DLC, such as boron-doped diamond, pyrolyzed photoresist films, and others known in the art.

[0077] In some examples, the first conductive layer and / or the second conductive layer can each independently comprise a two-dimensional material. Examples of two-dimensional materials are described, for example, by Giem et al., Nature, 2013, 499, 419-425, which is hereby incorporated herein by reference for its description of two-dimensional materials. The two- dimensional material can, for example, comprise graphene, a transition metal di chalcogenide, or a combination thereof. As used herein, a “transition metal dichalcogenide” refers to a compound comprising a transition metal and two chalcogen atoms. As used herein, a “transition metal” refers to any element from groups 3-12, such as Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, La, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, and Ac. As used herein a “chalcogen” refers to any element from group 16, such as oxygen, sulfur, selenium, tellurium, and polonium. As such, transition metal chalcogenides can include transition metal oxides, transition metal sulfides, and transition metal selenides, among others. For example, the transition metal di chalcogenide can comprise M0S2, WS2, MoSe2, WSe2, MoTe2, WTe2, ZrS2, ZrSe2, NbSe2, NbS2, TaS2, TiS2, NiSe2, EfoSes, or a combination thereof.

[0078] In some examples, the first conductive layer comprises graphene, such as monolayer graphene or multi-layered graphene. In some examples, the second conductive layer comprises graphene, such as monolayer graphene or multi-layered graphene. In some examples, the first conductive layer and the second conductive layer both comprise graphene. In some examples, the first conductive layer and the second conductive layer both comprise multi-layered graphene.

[0079] In some examples, the first conductive layer and the second conductive layer are substantially the same. In some examples, the first conductive layer and the second conductive layer are different.

[0080] The first insulating layer and the second insulating layer can each independently comprise any suitable two-dimensional material. Examples of two-dimensional materials are described, for example, by Giem et al., Nature, 2013, 499, 419-425, which is hereby incorporated herein by reference for its description of two-dimensional materials. The two- dimensional material can, for example, comprise hexagonal boron nitride (h-BN), a transition metal di chalcogenide, or a combination thereof. As used herein, a “transition metal dichalcogenide” refers to a compound comprising a transition metal and two chalcogen atoms. As used herein, a “transition metal” refers to any element from groups 3-12, such as Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, La, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, and Ac. As used herein a “chalcogen” refers to any element from group 16, such as oxygen, sulfur, selenium, tellurium, and polonium. As such, transition metal chalcogenides can include transition metal oxides, transition metal sulfides, and transition metal selenides, among others. For example, the transition metal di chalcogenide can comprise M0S2, WS2, MoSe2, WSe2, MoTe2, WTe2, ZrS2, ZrSe2, NbSe2, NbS2, TaS2, TiS2, NiSe2, EfoSes, or a combination thereof.

[0081] In some examples, the first insulating layer comprises hexagonal boron nitride, such as monolayer hexagonal boron nitride or multi-layered hexagonal boron nitride. In some examples, the second insulating layer comprises hexagonal boron nitride, such as monolayer hexagonal boron nitride or multi-layered hexagonal boron nitride. In some examples, the first insulating layer and the second insulating layer both comprise hexagonal boron nitride.

[0082] In some examples, the first conductive layer and the second conductive layer both comprise graphene and the first insulating layer and the second insulating layer both comprise hexagonal boron nitride.

[0083] In some examples, the first insulating layer has an average thickness of 1 nanometer (nm) or more (e.g., 1.25 nm or more, 1.5 nm or more, 1.75 nm or more, 2 nm or more, 2.25 nm or more, 2.5 nm or more, 2.75 nm or more, 3 nm or more, 3.25 nm or more, 3.5 nm or more, 3.75 nm or more, 4 nm or more, 4.25 nm or more, or 4.5 nm or more). In some examples, the first insulating layer has an average thickness of 5 nanometers (nm) or less (e.g., 4.75 nm or less, 4.5 nm or less, 4.25 nm or less, 4 nm or less, 3.75 nm or less, 3.5 nm or less, 3.25 nm or less, 3 nm or less, 2.75 nm or less, 2.5 nm or less, 2.25 nm or less, 2 nm or less, 1.75 nm or less, or 1.5 nm or less). The average thickness of the first insulating layer can range from any of the minimum values described above to any of the maximum values described above. For example, the first insulating layer can have an average thickness of from 1 nanometer to 5 nanometers (e.g., from 1 to 3 nm, from 3 to 5 nm, from 1 to 2 nm, from 2 to 3 nm, from 3 to 4 nm, from 4 to 5 nm, from 2 to 5 nm, from 1 to 4 nm, from 1.5 to 3.5 nm, or from 2 to 4 nm). In some examples, the first insulating layer can have an average thickness of from 1.5 to 3.5 nanometers. In some examples, the first insulating layer can have an average thickness of from 1 to 3 nanometers.

[0084] In some examples, the first insulating layer comprises hexagonal boron nitride and has an average thickness of from 1 nanometer to 5 nanometers. In some examples, the first insulating layer comprises hexagonal boron nitride and has an average thickness of from 1.5 to 3.5 nanometers. In some examples, the first insulating layer comprises hexagonal boron nitride and has an average thickness of from 1 to 3 nanometers.

[0085] In some examples, the second insulating layer has an average thickness of 1 nanometer

[0086] (nm) or more (e.g., 1.25 nm or more, 1.5 nm or more, 1.75 nm or more, 2 nm or more, 2.25 nm or more, 2.5 nm or more, 2.75 nm or more, 3 nm or more, 3.25 nm or more, 3.5 nm or more,

[0087] 3.75 nm or more, 4 nm or more, 4.25 nm or more, or 4.5 nm or more). In some examples, the second insulating layer has an average thickness of 5 nanometers (nm) or less (e.g., 4.75 nm or less, 4.5 nm or less, 4.25 nm or less, 4 nm or less, 3.75 nm or less, 3.5 nm or less, 3.25 nm or less, 3 nm or less, 2.75 nm or less, 2.5 nm or less, 2.25 nm or less, 2 nm or less, 1.75 nm or less, or 1.5 nm or less). The average thickness of the second insulating layer can range from any of the minimum values described above to any of the maximum values described above. For example, the second insulating layer can have an average thickness of from 1 nanometer to 5 nanometers (e.g., from 1 to 3 nm, from 3 to 5 nm, from 1 to 2 nm, from 2 to 3 nm, from 3 to 4 nm, from 4 to 5 nm, from 2 to 5 nm, from 1 to 4 nm, from 1.5 to 3.5 nm, or from 2 to 4 nm). In some examples, the second insulating layer can have an average thickness of from 1.5 to 3.5 nanometers. In some examples, the second insulating layer can have an average thickness of from 1 to 3 nanometers.

[0088] In some examples, the second insulating layer comprises hexagonal boron nitride and has an average thickness of from 1 nanometer to 5 nanometers. In some examples, the second insulating layer comprises hexagonal boron nitride and has an average thickness of from 1.5 to

[0089] 3.5 nanometers. In some examples, the second insulating layer comprises hexagonal boron nitride and has an average thickness of from 1 to 3 nanometers.

[0090] In some examples, the first insulating layer and the second insulating layer together have a total average thickness of 2 nanometers (nm) or more (e.g., 2.25 nm or more, 2.5 nm or more,

[0091] 2.75 nm or more, 3 nm or more, 3.25 nm or more, 3.5 nm or more, 3.75 nm or more, 4 nm or more, 4.25 nm or more, 4.5 nm or more, 4.75 nm or more, 5 nm or more, 5.25 nm or more, 5.5 nm or more, 5.75 nm or more, 6 nm or more, 6.25 nm or more, 6.5 nm or more, 6.75 nm or more, 7 nm or more, 7.25 nm or more, 7.5 nm or more, 7.75 nm or more, 8 nm or more, 8.25 nm or more, 8.5 nm or more, 8.75 nm or more, 9 nm or more, 9.25 nm or more, or 9.5 nm or more). In some examples, the first insulating layer and the second insulating layer together have a total average thickness of 10 nanometers (nm) or less (e.g., 9.75 nm or less, 9.5 nm or less, 9.25 nm or less, 9 nm or less, 8.75 nm or less, 8.5 nm or less, 8.25 nm or less, 8 nm or less, 7.75 nm or less,

[0092] 7.5 nm or less, 7.25 nm or less, 7 nm or less, 6.75 nm or less, 6.5 nm or less, 6.25 nm or less, 6 nm or less, 5.75 nm or less, 5.5 nm or less, 5.25 nm or less, 5 nm or less, 4.75 nm or less, 4.5 nm or less, 4.25 nm or less, 4 nm or less, 3.75 nm or less, 3.5 nm or less, 3.25 nm or less, 3 nm or less, 2.75 nm or less, or 2.5 nm or less). The total average thickness of the first insulating layer and the second insulating layer together can range from any of the minimum values described above to any of the maximum values described above. For example, the first insulating layer and the second insulating layer together have a total average thickness of from 2 to 10 nanometers (e.g., from 2 to 6 nm, from 6 to 10 nm, from 2 to 4 nm, from 4 to 6 nm, from 6 to 8 nm, from 8 to 10 nm, from 2 to 9 nm, from 2 to 8 nm, from 2 to 7 nm, from 2 to 5 nm, from 3 to 10 nm, from 4 to 10 nm, from 5 to 10 nm, from 7 to 10 nm, from 3 to 9 nm, from 4 to 8 nm, or from 3 to 7 nm). In some examples, the first insulating layer and the second insulating layer together have a total average thickness of from 3 to 7 nanometers. In some examples, the first insulating layer and the second insulating layer together have a total average thickness of from 4 to 6 nanometers. In some examples, the total average thickness of the first insulating layer and the second insulating layer together is sufficient to suppress any direct tunneling between the first conductive layer and the second conductive layer in the absence of the impurity.

[0093] In some examples, the first insulating layer and the second insulating layer both comprise hexagonal boron nitride, and the first insulating layer and the second insulating layer together have a total average thickness of from 2 to 10 nanometers. In some examples, the first insulating layer and the second insulating layer both comprise hexagonal boron nitride, and the first insulating layer and the second insulating layer together have a total average thickness of from 3 to 7 nanometers. In some examples, the first insulating layer and the second insulating layer both comprise hexagonal boron nitride, and the first insulating layer and the second insulating layer together have a total average thickness of from 4 to 6 nanometers.

[0094] In some examples, the first insulating layer and the second insulating layer both comprise hexagonal boron nitride, and the total average thickness of the first insulating layer and the second insulating layer together is sufficient to suppress any direct tunneling between the first conductive layer and the second conductive layer in the absence of the impurity.

[0095] In some examples, the first insulating layer and the second insulating layer are substantially the same. In some examples, the first insulating layer and the second insulating layer are different.

[0096] In some examples, the impurity comprises a quantum system.

[0097] In some examples, the impurity comprises a defect, such as a vacancy, an interstitial defect, a dopant, or a combination thereof.

[0098] In some examples, the impurity comprises a metal atom, such as a metal selected from the group consisting of Er, Mn, Pt, Fe, V, Cu, Co, Yb, Pr, Eu, and combinations thereof.

[0099] In some examples, the impurity comprises a molecule. The molecule can comprise any suitable molecule. For example, the molecule can comprise any molecule that can be deposited as a thin film (e.g., down to a fractional monolayer) and has electronic states in the range of ± 3V. In some examples, the impurity comprises a molecule, such as a macrocyclic ligand. In some examples, the impurity comprises a molecule, such as a porphyrin, a corrole, a phthalocyanine, or a combination thereof. In some examples, the molecule comprises a metalligand molecule, such as a metal porphyrin, a metal corrole, a metal phthalocyanine, or a combination thereof, wherein the metal can, for example, comprise Cu, V, Co, Fe, Mn, Zn, Ni, Cr, Ti, or a combination thereof. In some examples, the impurity comprises a molecule, such as copper phthalocyanine, vandyl phthalocyanine, or a combination thereof. In some examples, the impurity comprises a molecule, such as one or more of those shown in Figure 4.

[0100] In some examples, the impurity comprises a third two-dimensional material, optionally further comprising a defect therein. For example, the impurity can comprise a layer of a transition metal dichalcogenide, such as M0S2, optionally further comprising a defect therein.

[0101] In some examples, the device further comprises a first electrode disposed on and in electrical and physical contact with at least a portion of the first conductive layer. The first electrode can comprise any suitable material, such as those known in the art. In some examples, the first electrode comprises a metal, such as gold, and / or a magnetic material.

[0102] In some examples, the device further comprises a second electrode disposed on and in electrical and physical contact with at least a portion of the second conductive layer. The second electrode can comprise any suitable material, such as those known in the art. In some examples, the second electrode comprises a metal, such as gold, and / or a magnetic material.

[0103] In some examples, the tunnel junction device is a qubit.

[0104] In some examples, the tunnel junction device comprises a small number (e.g., 1000 or less) of impurities within a solid state device.

[0105] Methods of Making

[0106] Also disclosed herein are methods of making any of the devices disclosed herein. For example, the methods can comprise, in any order: disposing the first insulating layer on at least a portion of the first conductive layer; disposing the impurity on the first insulating layer or the second insulating layer; disposing at least a portion of the first insulating layer on at least a portion of the second insulating layer to substantially encapsulate the impurity; disposing the second insulating layer on at least a portion of the first insulating layer; and disposing the second conductive layer on at least a portion of the second insulating layer.

[0107] Disposing the first conductive layer and / or the second conductive layer can, for example, comprise atomic layer deposition, chemical vapor deposition, electron beam evaporation, thermal evaporation, sputtering deposition, pulsed laser deposition, printing, lithographic deposition, spin coating, drop-casting, zone casting, dip coating, blade coating, spraying, slot die coating, curtain coating, mechanical exfoliation and dry transfer, or combinations thereof.

[0108] Disposing the first insulating layer and / or the second insulating layer can, for example, comprise mechanical exfoliation and / or dry transfer.

[0109] In some examples, disposing the first conductive layer, the first insulating layer, the second insulating layer, the second conductive layer, or a combination thereof comprises mechanical exfoliation and / or dry transfer.

[0110] Disposing the impurity can, for example, comprise atomic layer deposition, chemical vapor deposition, electron beam evaporation, thermal evaporation, sputtering deposition, pulsed laser deposition, printing, lithographic deposition, spin coating, drop-casting, zone casting, dip coating, blade coating, spraying, slot die coating, curtain coating, or combinations thereof. In some examples, disposing the impurity comprises drop casting, spin casting, thermal evaporation, or a combination thereof.

[0111] Articles and Methods of Use

[0112] Also disclosed herein are methods of use of any of the devices disclosed herein, for example in a system and / or an article. For example, the methods can comprise using the device in a quantum device, such as a quantum information system, a quantum computing device, a quantum sensor, a quantum transduction device, or a combination thereof.

[0113] Also disclosed herein are articles (e.g., articles of manufacture) comprising one or more of any of the devices disclosed herein. For example, the article can be a quantum device, such as a quantum information system, a quantum computing device, a quantum sensor, a quantum transduction device, or a combination thereof.

[0114] In some examples, the methods can comprise using the device to characterize the impurity. For example, the methods can comprise using ESR (e.g., pulsed ESR) to characterize the impurity.

[0115] A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, other embodiments are within the scope of the following claims.

[0116] The examples below are intended to further illustrate certain aspects of the devices and methods described herein, and are not intended to limit the scope of the claims.

[0117] EXAMPLES

[0118] The following examples are set forth below to illustrate the methods and results according to the disclosed subject matter. These examples are not intended to be inclusive of all aspects of the subject matter disclosed herein, but rather to illustrate representative methods and results. These examples are not intended to exclude equivalents and variations of the present invention which are apparent to one skilled in the art.

[0119] Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, temperature, etc.) but some errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, temperature is in °C or is at ambient temperature, and pressure is at or near atmospheric. There are numerous variations and combinations of measurement conditions, e.g., component concentrations, temperatures, pressures and other measurement ranges and conditions that can be used to optimize the described process.

[0120] Example 1 - 1 modular approach to monolithic integration, initialization, and readout for solid-state qubits

[0121] Described herein is a modular method for designing and creating tunnel junctions that can be used to electrically detect magnetic resonance in a variety of different zero-dimensional (OD) electronic systems. Briefly, the technique relies on the mechanical exfoliation and stacking of 2D sheets of graphene (gr) and hexagonal boron nitride (hBN) using established dry-transfer techniques to form a layer structure comprising gr / hBN / hBN / gr, with the hBN layers typically 1- 3 nm each and for a total hBN thickness of roughly 5 nm. The graphene layers can be either single-layer or multi-layer. These "bare" structures can be further modified by pausing fabrication after the first gr / hBN layer and deposition of intentional impurities such as metal atoms (Er, Mn, Pt, Fe, ...) or small molecules (such as copper phthalocyanine, CuPc; vandyl phthalocyanine, VOPc; ...). This encapsulation of arbitrary OD systems has not been previously demonstrated. Metal electrodes are then attached to the top and bottom graphene layers to allow for 2-terminal electrical transport.

[0122] In bare devices made with ultra-pure hBN there are no OD states, e.g., no point defects in the hBN and no impurities at the interface, and the differential conductance of the tunneling current (dl / dV) is smooth and featureless. In the presence of OD states within the hBN layer, resonances or peaks will appear in the dl / dV when the voltage between the two graphene electrodes brings the energy of those states into resonance with one of the graphene electrodes. These OD states can generally be broken down into 3 categories: 1) structural defects in the hBN (e.g., vacancies, interstitials, chemical doping), 2) small molecules intentionally introduced at the hBN / hBN interface (CuPc, VOPc,...), and 3) atomic impurities intentionally introduced at the hBN / hBN interface (Er, Mn, Fe, Pt, ...).

[0123] In devices showing resonances in dl / dV due to one of the three OD systems described above, one can generate a spin-blockade effect by adding a magnetic electrode to either the top or bottom graphene layer. This magnetic electrode can inject a spin polarized current into the impurity that can polarize the OD electronic state, suppressing further tunneling current. This then makes the conductivity of the tunnel junction sensitive to the spin state of the impurity (OD system). This sensitivity can be further exploited by the application of either continuous or pulsed microwave fields at the junction in the presence of an applied magnetic field. In this regime, the microwave excitation can drive magnetic resonance of the OD state, or conversely the electronic conductivity of the tunnel junction becomes an electrical readout of the magnetic resonance. A similar effect can be obtained in a device without magnetic electrodes but wherein the OD systems are paired to create a singlet / triplet spin system, with the relative orientation of the spins in the two OD systems controlling the creation / suppress! on of a spin blockade.

[0124] The dl / dV characterization of the devices described herein is consistent with other systems that have been shown to exhibit this spin blockade effect.

[0125] Taken together, this provides multiple channels for using these devices as quantum sensors and as a tool to characterize the electronic structure of small molecules and defect systems. The spin blockade effect can be read out using either DC or microwave techniques when an external magnetic field is applied. Since this approach allows access to all three types of OD system, this tunnel junction platform is modular and general, allowing for the investigation of candidate quantum systems that are not accessible through other techniques. For example, pure microwave techniques for measuring magnetic resonance typically require 1012molecules or atoms, or more, while these tunnel junctions can routinely sample 1,000s to 100s of 0D systems, with the potential to extend to single-system sensitivity.

[0126] The field of quantum sensing does not currently have a platform with this level of generality.

[0127] Further, the fact that this scheme allows for electrical readout (as opposed to microwave or optical readout, as is the standard in the field) allows for scaling to large arrays and integration with other technologies that is not possible with competing technologies. Sensing targets include both DC and high frequency electric and magnetic fields, charge and charge dynamics, molecular structure, and molecular dynamics.

[0128] Example 2 - A Generalized and Modular Approach to Tunnel- Junction Spectroscopy for Quantum Systems

[0129] Presented herein is a generalized and modular scheme for tunneling spectroscopy of 0D quantum systems based on the exfoliation and stacking of 2D heterostructures. In this scheme, layers of graphene / graphite (gr) and hexagonal boron nitride (hBN) are assembled into a gr / hBN / hBN / gr tunnel junction. The differential conductance (dl / dV) of this structure is sensitive to both direct tunneling through the insulating hBN and resonant tunneling through any impurity states within the bandgap. The ability to resolve a variety of structural defects in hBN as well as the direct observation of the HOMO and LUMO states of vanadyl phthalocyanine (VOPc) encapsulated at the interior hBN / hBN interface of the heterostructure were demonstrated (Figure 1). The VOPc tunneling spectra directly correlate with scanning tunneling microscopy (STM) of witness samples and are consistent with density functional theory (DFT) of VOPc. This technique is extensible to a wide variety of OD systems encapsulated at the hBN / hBN interface, including electrically (or redox) active molecular systems, adatoms, and point defects in 2D materials. This generality and flexibility provides an exciting opportunity for both electronic / structural characterization of these quantum states as well as potential applications in quantum information.

[0130] Example 3 - Defect-assisted electron tunneling in 2D Van der Waals heterostructures

[0131] Defect-assisted resonant electron tunneling in hexagonal boron nitride (hBN) is demonstrated via electron transport measurements of graphene / hBN / graphene tunnel junctions. This study reveals distinct resonance peaks in the differential conductance (dl / dV) corresponding to native defect states in hBN. Tunneling was investigated in devices fabricated from three sources of hBN and substantial variation was seen in defect density and electronic activity depending on the source and synthesis method. Further, hBN grown with excess carbon in the reaction chamber shows the emergence of sharp features typically associated with tunneling through point defects. These features are stable on sweep up / down and their temperature dependence reveals thermal broadening that allows for the inference of a zero-temperature inhomogeneously broadened linewidth of 9 meV. These results validate this modular platform as a tool for investigating tunneling spectroscopy of atomic defects in 2D materials generally, for example a single layer of a transition metal di chalcogenide such as M0S2 could be inserted between the two insulating hBN layer. Given recent interest in these systems as potential qubits, has a significant potential impact for emerging applications in quantum information.

[0132] Example 4

[0133] Overview: A general framework can be developed for the integration of molecular spinbased qubits into solid state architectures, harnessing the ability to tune quantum states in molecular systems via synthetic control of ligand fields and electron-nuclear spin coupling to demonstrate a uniquely powerful approach to generating qubits-by-design. Both electron and nuclear spin qubits have been demonstrated in molecular systems [1-4], including work showing ms-level electronic spin coherence times in qubits with appropriately engineered ligands [5], This performance is comparable to other leading qubit systems based on diamond NV centers [6- 8], silicon donors [9-13], and Josephson junctions, and has the unique benefit of enabling chemical tuning to tailor the coherence properties for particular applications. However, the field has thus far relied on measurements of large ensembles in solution, precluding the study of single-qubit properties and impeding scaling and integration with existing and emerging quantum technologies. Addressing this challenge requires an interdisciplinary program that exploits a framework of spin-dynamical theory and modeling to bridge from the synthesis of chemical qubits, to the validation of their quantum coherent properties, to the ultimate goal of quantum coherent device engineering. This approach must make connections across length scales and traditional disciplinary boundaries in order to understand the potential and challenges associated with each component. Collectively, this work can establish a pathway for rapid feedback on the evolving understanding of how the requirements of quantum functionality intersect with the phase spaces accessible to molecular design and synthesis at one extreme and device design and fabrication at the other. As it matures, this framework can develop into a roadmap for the design of molecule-based quantum-functional devices that can be of broad relevance to the quantum information community and provide guidance as to how moleculebased quantum devices can be most effectively integrated into larger quantum-functional architectures.

[0134] Previous research

[0014] , focused on integrating molecular materials into solid-state architectures via the fabrication of molecular tunnel junctions (MTJs), providing a potential paradigm for achieving these goals. However, this approach is limited by two critical technical constraints: i) placing the top contact in a vertical MTJ without damaging the molecule, and ii) identifying the molecular response in the presence of transport artifacts. This work will address these challenges by exploiting recent advances in the mechanical transfer of 2D materials to prevent heat damage, filament formation, and chemical reactivity due to the electrodes while also protecting the qubits from the ambient environment.

[0135] Integration of Molecular Qubits into Solid-State Devices: Past work has demonstrated that mechanical stacking of a 2D sheet such as graphene on an atomically-flat substrate can capture gases and / or liquids from the ambient environment. Though atomically thin, the graphene honeycomb lattice has been found to be impermeable to many gases, including helium

[0031] , Even though relatively weak, the mating of atomically-flat sheets at the edges by van der Waals forces is still strong enough to ‘seal in’ any encapsulated contents, and provides a mechanical pressure that is estimated to be on the GPa scale in some cases

[0032] , Such encapsulation has enabled scanned probe imaging of surface water layers

[0033] , and has recently led to the imaging of crystalline ice at room temperature

[0034] , Inspired by these observations, the fabrication process described herein relies on the ability to exfoliate and deterministically transfer single to few layer stacks of van der Waals materials such as graphene and h-BN. To that end, a cluster of transfer tools have been developed based on the “dry” transfer technique wherein 2D sheets are exfoliated onto a supporting substrate which is then coated with a sacrificial polymer layer. This polymer layer can then be mechanically peeled from the substrate support, taking the 2D flakes with it, and mechanically transferred to the target substrate, enabling the facile fabrication of hybrid devices.

[0136] The complete process flow for device fabrication is outlined in Figure 2. The bottom electrode is comprised of a patterned CVD-graphene layer that has been metalized with Au contacts. Next, the tunneling layer is fabricated on a secondary substrate where an appropriate h- BN flake is identified. The thickness of candidate flakes will be determined with atomic-force microscopy (AFM) with flake thickness of 1-2 ML allowing for some tunneling directly through the h-BN layer and 5-10 ML achieving complete electrical isolation between top and bottom electrodes. This h-BN flake will be transferred onto the patterned CVD-graphene transport channel prior to the deposition of the molecular qubits candidates (e.g., via drop-casting, spincoating, thermal evaporation, etc.) and subsequently capped by a second, exfoliated, hBN flake and then a second, exfoliated graphene flake. This molecular deposition and encapsulation can occur completely within an Ar-purged glovebox, allowing the use of oxygen and moisturesensitive molecular species.

[0137] Synthetic Control of Quantum Functionality: The facile synthetic tunability of molecular systems enables the design of molecules that are targeted towards incorporation into the systems described herein. Within this approach the scientific questions of interest can be broken into broad two categories: (i) spin-based interactions within the molecules and (ii) the molecule-device interface. For the specific molecules proposed here, a focus is on modulating the spin bearing atom, thereby influencing its addressability and its proximity to nuclear spins. The distance and type of nuclear spins can be tuned, for example selecting a proton vs. a halide. First, the frequency and width of the EPR transition can be modified by careful selection of the metal center; for example copper, with its large g- value, will decrease the frequency of the transition

[0023] , Once a transition metal is selected, its environment can be tuned. For example, this work can use macrocyclic ligands. Macrocycles offer a controlled environment for the metal-based spin center. Here, by using a chelating ligand that binds at multiple sites, the geometry of the molecule will be preserved between the solid-state and solution. This has advantages for system integration, and creates two sets of distinct chemical sites for structural modification. By leveraging the atomic precision inherent in chemical synthesis, the distance between electronic and nuclear spin can be modulated by harnessing these specific functionalizable positions, previous research demonstrating this is shown in Figure 3 [1], Progressing from protons to halides is synthetically straightforward. Larger moieties, such as aryl groups, can also be appended, engendering larger separations.

[0138] Turning to the second category, there are two viable pathways to promote system integration: surface deposition and solution-based measurement. For surface deposition, achieved using approaches such as drop casting or sublimation, the first consideration will be designing planar molecules. Planar molecules will not dramatically structurally distort on a surface, thereby enabling the use of ensemble measurements as a proxy for future surface studies

[0040] , For surface deposition and sublimation an additional design criterion will be charge neutral molecules. Here, macrocycles will be very useful as anionic ligands that can be paired with the correctly charged transition metal ion. For example, corroles are well suited to supporting tricationic metal species, while systems such as porphyrins are ideal for dicationic metal centers [41-43], The wealth of macrocyclic ligands with functionalizable sites makes this an excellent initial target family of molecules [44-46],

[0139] Chemical Qubit Synthesis: The ability to tune quantum states in molecular systems via synthetic control of ligand fields and electron-nuclear spin coupling provides a uniquely powerful approach to generating qubits-by-design. This potential encompasses both the ability to optimize specific quantum parameters, such as the coherence time of electron and nuclear spin states, as well as to develop pathways for coherent communication between qubits (i.e. via tuning the hyperfine interaction to control coupling between electronic and nuclear qubits or the development of di-nuclear molecules and conjugated molecular networks to explore electronelectron spin coupling). The potential impact of this strategy for applications in molecular-scale quantum sensing, such as the local measurement of magnetic fields and in situ biological sensing, are well documented [66, 67] but extending the reach of these molecular qubits to include solid-state applications requires an integrated and interdisciplinary effort. For example, electron spin lifetimes of the order of milliseconds have been demonstrated in tailored molecules [5] making them attractive candidates for quantum memory applications if a mechanism for solid-state initialization and readout can be established.

[0140] From a synthetic point of view, realizing this potential requires understanding of the design parameters for these systems and how they should be optimized for functionality in a solid-state environment. For example, long-lived electron spin based qubits need to be created and the ideal proximity between electronic and nuclear spins needs to be determined to execute coherence transfer experiments without destroying coherence time. By integrating with theory, the impact of modulating the electronic structure of a molecule on coherence time can be predicted. Then new molecules can be synthesized and aggregate measurements can be performed on them using traditional magnetic resonance spectroscopies such as EPR, NMR, and ENDOR. Subsequently, these aggregate measurements can be compared with studies of small ensembles in functional devices and single-molecules via STM. The integration of these approaches can enable uncovering the fundamental design principles for creating molecular qubits, with particular emphasis on understanding how to balance the constraints of singlemolecule quantum functionality with the characteristics that optimize solid-state initialization and readout, all while minimizing parasitic effects leading to decoherence.

[0141] Herein, the development of two series of molecules is described, one designed to probe ligand field effects on the electronic spin-based properties of a molecule, the second designed to probe nuclear-electronic spin coupling. In the first series, transition metals in the di-and tri- valent oxidation states in ligand scaffolds such as porphyrins and corroles can be explored. First, a series of neutral molecules featuring these ligands can be studied, as these are most amenable to ultra-high vacuum deposition. The electron donating ability of these systems is also highly dependent on ring substituents. Further, the planar nature of the molecules enables the addition of ligands to the axial positions, allowing for further tuning of electronic properties via modulation of the relative energy of the tZ-orbitals (Figure 4) [68, 69], Several targets are vanadyl, copper, cobalt, and iron complexes of the ligands shown in Figure 4.

[0142] In the second series, electron nuclear coupling can be explored. Here, the periphery of the conjugated macrocyclic molecules (e.g., Figure 4) can be decorated with different nuclear spin bearing atoms and the impact of the nuclear spin coupling on the electronic spin resonance of the central transition metal ion can be probed. Within this modular structure,1H,19F, and35C1 nuclei can be incorporated, and their distance from the metal center can be tuned by appending these atoms to different positions on the exterior of the rings (positions Xa-d in Figure 4). Each of these nuclei has a different nuclear magnetic moment, thereby tuning the strength of the magnetic coupling between the metal center and the nuclear spin. Molecules can be characterized by X-ray crystallography by techniques that are capable of comparing structure in solution and the solid state, for example FT-IR spectroscopy and UV-Vis / diffuse reflectance spectroscopy. Once the molecules are structurally characterized, straightforward ensemble EPR characterization can be performed for comparison to single molecule and small ensemble measurements. CW characterization can be accessed through local user facilities. Pulse measurements can also be executed.

[0143] Quantum Coherent Device Engineering: Building on the fabrication of hybrid molecular / solid-state devices

[0014] , present herein is a program that leverages recent breakthroughs in molecular encapsulation using mechanical transfer of 2D materials (described above) to fabricate and study molecule-based quantum functional devices. Using ED-EPR techniques , spin lifetime, electron g-factor, and hyperfine coupling for small ensembles of molecules trapped in the devices can be studied. These measurements can be referenced to bulk ensemble measurements and single molecule studies to determine sources of decoherence unique to the fully-encapsulated device structure. This information can in turn inform future rounds of qubit design and synthesis . As the understanding of these systems matures, this effort can be expanded to include a magnetic electrode into the MTJs. These structures can allow operation in a two-tone magnetic resonance mode wherein ferromagnetic resonance (FMR) is excited in the magnetic electrode at the same time as EPR of the qubit. This can be approximated as a CW analogue for DEER protocols in pulse-EPR where the second electron is replaced by the magnetic electrode. As shown in previous work

[0022] this mode of operation allows for the pumping of a pure spin current (i.e. spin flow in the absence of charge flow) into the encapsulated qubits, raising the possibility of new approaches to coherent initialization of the quantum state of the qubits.

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[0185] Example 5 - A general and modular approach to solid-state integration and readout of zero-dimensional quantum systems

[0186] Electronic spectroscopy of zero-dimensional (0D) quantum systems, including point defects in solids [A1-A3], atomic states [A4, A5], and small molecules [A6-A8], is an important tool for developing a fundamental understanding of these systems, with applications ranging from solid-state [A9] and molecular [A10, Al l] materials development to emerging technologies rooted in quantum information science [A12], Toward this end, scanning tunneling spectroscopy (STS) has demonstrated atomic-scale sensitivity, but is not easily scalable for applications, whereas device-based approaches rely on embedding these systems within a solid- state tunnel junction (TJ) and are not generally applicable. Herein, an all-electrical readout mechanism is demonstrated for these quasi -0D states that is modular and general, dramatically expanding the phase space of accessible quantum systems and providing an approach that is amenable to scaling and integration with other solid-state quantum technologies. The approach herein relies on the creation of high-quality tunnel junctions via the mechanical exfoliation and stacking of multi-layer graphene (MLG) and hexagonal boron nitride (hBN) to encapsulate the target quantum system (QS) in an MLG / hBN / QS / hBN / MLG heterostructure. This structure allows for electronic spectroscopy and readout of candidate quantum systems through a combination of Coulomb [Al 3-Al 5] and spin-blockade [Al 6, Al 7], providing access to entire classes of quantum systems that have previously only been accessible via optical spectroscopy or magnetic resonance measurements of large ensembles, if at all.

[0187] The power and modularity of this approach is demonstrated by the consideration of both intrinsic and encapsulated quantum systems in the form of point defects in hexagonal boron nitride (hBN) and the molecular qubit vanadyl phthalocyanine (VOPc), a spin 1 / 2 molecular qubit that has demonstrated long coherence times in an isostructural diamagnetic host (up to 1 ps at room temperature [A8]), respectively. The differential conductance (dl / dV) of these devices reveals the underlying electronic structure, and in the case of VOPc devices, both qualitative and quantitative agreement were confirmed with STS measurements and the theory of VOPc electronic structure [Al 8], These devices are fully compatible with existing solid-state quantum technologies (e.g., silicon quantum dots [Al 9] and superconducting qubits [A20]) and experimental protocols [A21-A23], and the fabrication protocols are compatible with monolithic integration of microwave components. These results therefore demonstrate a modular and general approach to the investigation and manipulation of new quantum systems that will allow for a more systematic approach to the design and manufacturing of new quantum technologies. For example, the motion of charge through a OD structure involves, at least temporarily, an initial and / or final state that possesses spin; study of this transport, especially in small magnetic fields, has been used to reveal quantum-technology-relevant quantities such as low-temperature spin coherence times in individual quantum dots [A24, A25], and at room temperature the hyperfine fields and exchange interactions of small numbers of defects [A26-A28],

[0188] There are several key constraints to consider for the integration of quantum systems into a device architecture to ensure its efficacy: (i) the relevant quantum properties should be preserved in the integrated state, (ii) the electronic response of the integrated device should allow for readout of the relevant quantum properties, (iii) the quantum system should be protected from fabrication processes, (iv) the device architecture should be compatible with existing quantum technologies. Mechanical exfoliation and stacking of 2D materials provide a low- temperature and nonreactive approach to building modular tunnel junctions with the potential to satisfy these criteria. The mechanical nature of 2D exfoliation and stacking provides facile encapsulation of quantum systems between 2D layers, including molecules, adatoms, and quantum point defects (QPD), that avoids the high temperatures and reactive chemistries typically involved in traditional fabrication processes. Further, exfoliation and stacking provide a facile route to the fabrication of high-quality tunnel junctions with atomically precise control of barrier thickness and strongly suppressed pinhole formation. Prior work in related tunnel junctions in the Coulomb blockade regime has demonstrated the potential for high-fidelity quantum readout [A16, A29, A30], Finally, this approach leverages a large body of prior work in integrating 2D materials into existing quantum architectures such as on-chip microwave resonators [A31], transmons [A32], and spin qubits [A19, A30],

[0189] Figure 6A shows a schematic illustration of one such hBN-based 2D tunnel junction (2D- TJ) device (see Supplementary Note SI for a more detailed discussion) with graphitic contacts and gold electrodes. The active area of the device is stacked with mechanically exfoliated hBN and graphite using well-established dry transfer techniques [A33 ], wherein the graphitic contacts include multilayer graphene (MLG) of typical thickness 6.5 ± 3.5 nm, well into the bulk graphitic regime. To achieve the desired tunneling conditions, the insulating hBN layer is selected to be between 1.5 nm and 3.5 nm, confirmed by atomic force microscopy (AFM) (Figure 10A). The thickness of the hBN barrier dictates the current of the nonlinear tunneling response, ranging from tens of nanoamps to a few microamps in this regime. Gold electrodes are deposited onto completed stacks, with care taken to avoid extending the metal electrodes over the active area of the device in order to suppress metal migration and the creation of parasitic current pathways. Figure 6B shows an optical image of a representative 2D-TJ device with an hBN tunnel barrier of 3.01 ± 0.66 nm and an active area of 3.1 pm2.

[0190] Initial device characterization is performed at room temperature, as shown in Figure 6C for a device constructed with hBN sourced commercially from HQ Graphene (thickness of 4 ± 0.5 nm). A schematic energy diagram is shown in the inset. The black curve shows the tunneling current through the device while sweeping the bias voltage (I-V response), revealing a contribution from direct tunneling through the barrier and additional tunneling processes within the device (e.g., the plateau at a source-drain bias of ± 0.30 V). To highlight these additional processes, synchronous measurement of dl / dV is performed using frequency modulation and homodyne detection with a lock-in amplifier, as represented by the purple curve in Figure 6C. These data show both direct tunneling and broad peaks that appear at, for example, ± 0.30 V and ± 0.60 V, suggesting the presence of resonant tunneling processes through quantum states with energies lying within the bandgap of the hBN.

[0191] To resolve these resonances, additional measurements were performed at a temperature of 15 K (purple curve in Figure 7A) for a similar device (hBN thickness of 3.01 ± 0.66 nm), and the reduction in thermal broadening reveals additional structure in the resonances that appear at ± 0.2 V and ± 0.50 V. The probability of direct tunneling depends on the thickness of the tunnel barrier and is suppressed exponentially with increasing tunnel barrier thickness (Figure 10B), so each peak in Figure 7A (purple data) could in principle represent either elastic defect-assisted tunneling, inelastic phonon-assisted tunneling, or some combination of the two. To further characterize these resonances, two additional sets of devices are investigated. The second set of devices is constructed using hBN synthesized [A34] (see Supplementary Note S2) at Ames National Lab (blue curve; hBN thickness of 1.66 ± 0.33 nm and area of 4.72 pm2). While the relative amplitude of the tunneling resonances changes as compared to the commercially-supplied hBN, it is notable that the position (voltage) of many of the peaks reproduces, for example, the symmetric resonant peaks around ± 0.21 V and similar peaks around -0.55 V, -0.3 V, and ±0.73 V. The third set of devices is constructed with ultra-pure hBN synthesized at the International Center for Materials Nano Architectonics (MANA) [A35] (green curve; hBN thickness of 2.01 ± 0.33 nm and area of 2.09 pm2). This material is known to yield devices with extremely high electron mobility when used to isolate, e.g., single-layer graphene from its environment, suggesting an exceptionally low level of charge-active defects [A36] . This hypothesis is borne out by dl / dV measurements, which show strong suppression of resonant tunneling as compared to the first two devices (a single weak resonance is observed at -0.23 V, as shown in Figure 11).

[0192] These results confirm that the tunneling resonances observed in both commercial and Ames Lab synthesized hBN are due to intrinsic defects within the hBN material and not extrinsic impurities or contamination. As detailed in Supplementary Note SI, this stacking process ensures a clean hBN interface without chemical exposure. Moreover, during the annealing process, thermal changes are gradual to prevent structural and functional alterations in the 2D layers caused by thermal shock. The rich variety of predicted structural defects predicted for hBN makes a definitive assignment of these resonances to specific atomic structures difficult. For example, prior work in modeling defect formation in hBN predicts the formation of native defects such as vacancies, antisites, and interstitial structural defects during hBN growth, with the most energetically favorable being carbon, oxygen, and hydrogen impurities [A37- A39], Further, each defect can in principle generate multiple peaks, for example, boron vacancies (VB) have multiple different charge states: e.g., neutral, -1, and -2, with Csv symmetry for the neutral and -2 states and D311 in the -1 state [A39], Finally, the commercially supplied hBN is polycrystalline, potentially leading to varying orientations within the TJ for chemically identical defect states. However, the reproducibility across two different sets of materials synthesized in two different laboratories (commercial and Ames hBN) provides strong evidence that these resonances do in fact arise from hBN defects. In addition, the absence of the peaks in the tunneling spectra from MANA hBN further supports the absence of impurities from residues deposited during our fabrication process or other extrinsic contamination. These measurements indicate that hBN-TJs can provide a sensitive probe of the electronic structure of atomic defects in the tunnel barrier. To further test this proposition, additional hBN crystals are prepared at Ames lab wherein carbon has been introduced during hBN growth (see Supplementary Note S2). This excess carbon can contribute to the creation of substitutional and interstitial carbon defects as well as C-nucleated and C-catalyzed defects [A37, A38, A40], Tunneling spectra from a device fabricated from this material are shown in Figure 7B, where an additional constellation of extremely sharp tunneling resonances is revealed. These peaks are highly reproducible, both the main figure and the inset show trace / re- trace scans of dl / dV confirming these sharp features are stable and well-defined states. Further analysis shows that individual peaks show thermal broadening, consistent with tunneling spectroscopy of atomic point defects (Figure 12A-Figure 12C).

[0193] These results demonstrate the facility with which these 2D tunnel junctions can be used to measure detailed electronic tunneling spectra for quantum point defects and impurities within a solid-state host, suggesting that this architecture may be further generalized to include encapsulated quantum systems. Specifically, the molecular spin qubit VOPc was considered.8Metallophthalocyanines are known molecular semiconductors, generally demonstrate environmental stability, and can be sublimed using standard evaporation techniques [A8, A41] resulting in well-ordered films, making them attractive targets for device integration [A42, A43], To validate this potential for incorporation into the solid-state quantum devices described above, first VOPc [A44] (see Supplementary Note S3) thin films on a monolayer of hBN grown on highly-oriented pyrolytic graphite (HOPG) were studied using scanning tunneling microscopy (STM). VOPc was deposited under ultra-high vacuum conditions (-1E-9 mbar) [A45], with a deposition rate of ~1 monolayer / min determined by STM imaging [A46], Figure 8A and Figure 8B show the molecular structure of VOPc and a schematic representation of the STM geometry, illustrating the heterostructure formed by VOPc deposition on hBN / HOPG. Figure 8C displays an STM topography image of a thin film of VOPc measured at 5 K, revealing the self-assembly of VOPc into a well-ordered film on the surface of the hBN / HOPG substrate whose orientation is consistent with the schematic in Figure 8B. Consistent with the nominal deposition rate and prior STM studies [A47], this image suggests the film comprises a uniform bilayer of VOPc [A47], with a low density of defects such as molecular vacancies or 3rdlayer molecules.

[0194] Differential conductance spectra taken at selected positions within the layer at a temperature of 5 K are shown in Figure 8D. Clear peaks in the dl / dV are resolved, representing the HOMO, LUMO and excited states of the VOPc film [A48] at these distinct locations, with a weak direct tunneling background evident at higher tip-sample bias. The energies of the peaks corresponding to resonant tunneling vary with tip position, revealing spatial variation in the molecular orbitals involved in the tunneling process as shown in the spectra in Figure 8D. Furthermore, spatial variation is observed in STM images of bare hBN and dl / dV maps of the VOPc surface (Figure 13A-Figure 13C). This suggests that other factors, including the moire pattern of hBN / HOPG and local defects in both HOPG and hBN, could contribute to spatial variations in the local energy structure and density of states.

[0195] The STM images indicate that VOPc thin films should form high-quality barriers in hBN TJ devices. In order to test this prediction, VOPc heterostructures were assembled in a five-layer stack (MLG / hBN / VOPc / hBN / MLG; see Supplementary Note S4). This tunneling device was then characterized by both I-V and dl / dV measurements at a temperature of 15 K (Figure 8E), as with the MLG / hBN / MLG structures in Figure 7A-Figure 7B. The dl / dV response reveals a direct tunneling background similar to the response of MLG / hBN / MLG devices fabricated from MANA hBN, but with the addition of tunneling resonances at voltages above +1 V and below -2.0 V that appear as broad peaks in the dl / dV spectrum. These voltage values are in rough agreement with the molecular states observed in STM, and also electronic transitions in the theoretical literature [Al 8], but the peaks appear significantly broadened and a direct comparison is obscured by the relatively large direct tunneling background in the TJ device. Confirming these resonances result from VOPc molecular states, control measurements of a sample without VOPc showed only direct tunneling without any indication of resonance peaks.

[0196] To mimic the spatially averaged nature of the TJ devices, STS data were collected at different sites within the VOPc molecule and at different positions across the layer. These 21 tunneling spectra were then normalized to their maximum dl / dV signal and averaged together to generate the wine-colored curve in Figure 9. This process results in broadened peaks around -2V and + 1.5 V. To facilitate direct comparison, the direct tunneling contribution to Figure 8E was removed by fitting the curve to the Fowler-Nordheim model and subtracting it from the dl / dV response of the VOPc-TJ device (green curve, Figure 9). In this model, the direct tunneling current is given by (see Supplementary Note S5) [A49]:

[0197] The result of this fitting process for the VOPc device is shown as a black dashed line in Figure 8E, yielding i=9.41 eV and 2=0.15 for both positive and negative voltage. However, different parameters optimize the positive and negative voltage regions for fo (sample area), / o= l .6 / 1013and / o=2.6 / I Ol 3, respectively. The results of a similar analysis performed on the hBN devices discussed in Figure 7A are shown in Figure 14A-Figure 14C. The difference between this calculated direct-tunneling background and the experimental data is shown in Figure 9 (green curve). This residue highlights the major resonant tunneling features in the spectra, which can themselves be modeled using the following Gaussian function r(£) for each resonance, with a defect current given by [Al 4] (see Supplementary Note S5) : co

[0198] J — co

[0199] This analysis yields three resonances centered at voltages of +1.6 V, -1.1 V, and -2.05 V (Figure 9, black dashed curve).

[0200] Comparing the averaged STS data (wine-colored curve) with the background- subtracted tunnel junction response (green curve) reveals excellent agreement in both the gap (1.63 V) and the width of the heterogeneously broadened ensembles. This result strongly supports the hypothesis that the tunneling spectra from the tunnel junction represent a spatial average over the VOPc bilayer, with the peak width dominated by real variations in tunneling current as a function of position within the VOPc molecule and for different local configurations of the bilayer.

[0201] In summary, the encapsulation of quantum point defects and molecules within a tunnel junction constructed from 2D materials is demonstrated, establishing a versatile and modular technique that can be applied to a wide variety of quasi -0D quantum systems. The device structure protects the QPDs and molecules during the fabrication processes, prevents direct contact between metal contacts and the 0D quantum systems (pinholes), and enables a highly sensitive readout of the electronic states of the intrinsic defects and molecular states. Tunneling spectroscopy of carbon-related defects within a MLG / C-doped hBN / MLG tunnel junction device and VOPc molecular qubits encapsulated within a similar device structure (MLG / hBN / VOPc / hBN / MLG) were demonstrated. Tunneling spectroscopy of the former shows atomic-like resonance states of the intrinsic carbon-related defects in hBN, while the latter reveals broad resonance peaks in the VOPc films that are quantitively consistent with STS of HOPG / hBN / VOPc half-devices and theory predictions of electronic structure [Al 8], The relative ease of fabrication and protective encapsulation demonstrates a facile approach to electronic tunneling spectroscopy for small ensembles of quasi-OD quantum systems that should be of interest for a wide variety of molecular and solid-state systems. Further, when combined with the extensive literature demonstrating high-fidelity quantum readout of electronic and nuclear spin states in related solid-state systems [A16, A29, A30, A50], this work provides a clear path to a dramatic expansion in the phase space of potential quantum systems to include optically inert but electrically active QPDs, molecules, and adatoms and their straightforward integration with existing solid-state quantum technologies.

[0202] Supplementary Note SI: stacking and fabrication of hBN tunnel junction (hBN-TJ) devices. After exfoliation of graphite on the Si / SiC>2 substrate, the top and bottom MLG flakes with appropriate thickness and shapes were identified using an optical microscope. To create a stack of the heterostructure with 2D materials, the process was initiated by transferring the top MLG. This is accomplished by picking it up using a polycarbonate (PC) film coated on a polydimethylsiloxane (PDMS) stamp and a glass slide at a temperature of 90°C. Subsequently, hBN is transferred onto the top MLG flake, also picked up at a temperature of 90°C. This procedure ensures that the interfaces of the hBN layer remain clean, with no direct contact with solvents or polymers. In the final step, the top MLG / hBN layers are delicately placed onto the bottom MLG, previously exfoliated on a Si / SiC>2 substrate, at a temperature of 105°C. The entire stack is then heated to 150°C for about 10 minutes for the adhesion of the 2D heterostructure onto the substrate. After allowing the stack to cool, the polycarbonate (PC) film was dissolved by immersing the stack in chloroform for approximately 4 minutes, the duration was adjusted based on the amount of PC film present on the substrate. The subsequent step involves annealing the sample for a duration of 90 minutes at a temperature of 350°C under vacuum conditions. Specifically, a gradual thermal ramp-up and ramp-down was employed, with a 90-minute rise from room temperature to 350°C, 90 minutes of annealing at 350°C, followed by a 90-minute descent to room temperature to prevent thermal shock. This process eliminates any residues of polymers and solvents from the stack while enhancing the interfacial bonding between the layers of the stack. Electron beam lithography was employed to pattern gold contacts for establishing electrical connections. Following the spin coating of MMA and PMMA (both deposited at 3000 RPM for 45 seconds), electron beam was used to write the contact patterns. The pattern is then developed with a mixture of MIBK / IPA for approximately 70 seconds, adjusting the duration based on the amount of resist residue on the sample. Finally, a 5 nm Chromium (Cr) film is deposited, followed by a 150 nm layer of gold (Au) for the metal contacts. Acetone was utilized for the lift-off process of the gold. At the end the sample is wire-bonded on a chip carrier for transport measurements.

[0203] Supplementary Note S2: Ames hBN synthesis. Synthesis of hBN takes place in a high- pressure furnace at 3.2 GPa, in a process that co-synthesizes both hBN and MgB2. The temperature is increased to 1380°C before slowly cooling down to 650°C. The flux ratio of Mg:B elements in a BN crucible is 1 :0.7. The synthesis process for carbon dopped hBN is similar to that described above with the exception that 2% of the B is replaced by C, resulting in a flux ratio of Mg: B: C of 1 : 0.686: 0.014.

[0204] Supplementary Note S3: VOPc synthesis and characterization.

[0205] General Considerations: Vanadyl(IV) sulfate pentahydrate was purchased from Alfa Aesar, 1 -pentanol and phthalonitrile were purchased from Sigma- Aldrich, and diazabicyclo[5.4.0]undec-7-ene (DBU) was purchased from Chem-Impex International. All chemicals were used as received.

[0206] Synthesis: Vanadyl(IV) phthalocyanine (VOPc) was prepared according to an adapted literature procedure [SI], A 250 mL round-bottom flask was charged with vanadyl(IV) sulfate pentahydrate (0.7604 g, 3 mmol, 1.2 eq.), phthalonitrile (1.2817 g, 10 mmol, 4 eq.), DBU (1.5 mL, 10 mmol, 4 eq.), 40 mL 1-pentanol, and a stir bar. The flask was then refluxed at 145°C for 16 hours. The dark blue-purple product was isolated via vacuum filtration, rinsed with 100 mL deionized water, 100 mL ethanol, and 500 mL ethyl acetate, and dried for 20 minutes. Product yield was 0.2998 g (20.7%). MALDI-TOF mass spectrometry (m / z): [M]+calculated for C32H16N8VO, 579.089, 580.092, 581.095, 580.086; found 578.859, 579.037, 579.140, 579.919. FTIR (cm-1): 436.9, 504.9, 567.8, 637.9, 723.4, 750.2, 774.9, 800.7, 836.8, 872.8, 896.5, 958.4, 998.5, 1072.7, 1117.1, 1156.2, 1285.0, 1330.4, 1413.8, 1460.2, 1496.3, 1606.5, 3668.5, 3744.8, 3848.9.

[0207] Powder X-Ray Diffraction: Bulk purity was evaluated through powder X-ray diffraction (PXRD) (Figure 15). A powdery sample of VOPc was loaded into a PXRD mask between pieces of Kapton tape and PXRD patterns were collected on a STOE STADI MP diffractometer equipped with CuKal radiation ( = 1.5406 A) located at the Integrated Molecular Structure Education and Research Center of Northwestern University. Simulation of PXRD pattern was produced from crystallographic data previously collected [S2] .

[0208] Other Physical Measurements: MALDI-TOF mass spectrometry (MS) measurements were collected on a Bruker RapiFlex Tissue Typer mass spectrometer located at the Integrated Molecular Structure Education and Research Center of Northwestern University. No matrix was necessary for the ablation and desorption of VOPc in MALDI-TOF MS measurements. Infrared spectra were recorded on a Bruker Alpha II Compact FTIR spectrometer equipped with an attenuated total reflectance accessory located at the Department of Chemistry Instrumentation Facility of Massachusetts Institute of Technology.

[0209] Supplementary Note S4: stacking and fabrication of VOPc tunnel junction (VOPc- TJ) device. Heterostructures were assembled in a five-layer stack using a modification of the process described for MLG / hBN / MLG structures above: an initial layer of MANA hBN with target thickness of 1.5 nm was stacked onto a bottom MLG electrode, and then the polycarbonate film was removed using chloroform. This structure was transferred into the STM chamber for deposition of VOPc using an identical protocol to the one reported for STM studies above. The stack, now with VOPc as the top layer, was then removed from the STM chamber and a second MANA hBN layer (target thickness of 3.5 nm) and the top MLG electrode were placed on top with an alignment that prevents shorting of the two MLG layers, resulting in a stack structure of MLG / hBN(1.5 nm) / VOPc bilayer / hBN (3.5 nm) / MLG (see inset to Figure 8E).

[0210] Supplementary Note S5: direct tunneling and resonant tunneling models. In the direct tunneling model (Equation 1 above), lb is resonant tunneling current, the effective mass of electron in hBN [S3], 0.588mo, where m0is mass of free electron, q is charge of electron, h is Planck constant, E is energy, and / t=3.77 eV is chemical potential of graphene [S4], fo, fi, and fz are three free parameters. The parameter o rescales the current to match the effective area of the sample, and i is the effective height of the barrier which is generally the sum of the chemical potential and thermionic work function. The parameter fz modifies the applied electric field, to an effective F for this model.

[0211] In the resonant tunneling model (Equation 2), Id is resonant tunneling current, / (E) is Fermi-Dirac distribution, and Gaussian function for each resonance is: where do, di, and dz are the conductance peak height, voltage of the peak, and linewidth, respectively.

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[0263] EXEMPLARY ASPECTS

[0264] In view of the described compositions, devices, systems, and methods, herein below are described certain more particularly described aspects of the inventions. The particularly recited aspects should not, however, be interpreted to have any limiting effect on any different claims containing different or more general teachings described herein or that the “particular” aspects are somehow limited in some way other than the inherent meanings of the language and formulas literally used therein.

[0265] Example 1 : A modular design for a zero-dimensional (0D) state tunnel junction device comprising: a first conductive layer; a first insulating layer disposed on and in electrical and physical contact with at least a portion of the first conductive layer, the first insulating layer comprising a first two-dimensional material; a second insulating layer disposed on and in electrical and physical contact with at least a portion of the first insulating layer, such that at least a portion of the first insulating layer is sandwiched between at least a portion of the second insulating layer and at least a portion of the first conductive layer, the second insulating layer comprising a second two-dimensional (2D) material; an impurity sandwiched between and substantially encapsulated by the first insulating layer and the second insulating layer, the impurity being in electrical and physical contact with at least a portion of both the first insulating layer and the second insulating layer, the impurity comprising a defect, an atom, a molecule, or a combination thereof, wherein the impurity is a zero-dimensional (0D) system; and a second conductive layer disposed on and in electrical and physical contact with at least a portion of the second insulating layer, such that at least a portion of the second insulating layer is sandwiched between at least a portion of the first insulating layer and at least a portion of the first conductive layer.

[0266] Example 2: The device of any examples herein, particularly example 1, wherein the first conductive layer comprises a two-dimensional material. Example 3 : The device of any examples herein, particularly example 1 or example 2, wherein the second conductive layer comprises a two-dimensional material.

[0267] Example 4: The device of any examples herein, particularly examples 1-3, wherein the first conductive layer comprises graphene, such as monolayer graphene or multi-layered graphene.

[0268] Example 5: The device of any examples herein, particularly examples 1-4, wherein the second conductive layer comprises graphene, such as monolayer graphene or multi-layered graphene.

[0269] Example 6: The device of any examples herein, particularly examples 1-5, wherein the first conductive layer and the second conductive layer are substantially the same.

[0270] Example 7: The device of any examples herein, particularly examples 1-5, wherein the first conductive layer and the second conductive layer are different.

[0271] Example 8: The device of any examples herein, particularly examples 1-7, wherein the first insulating layer comprises hexagonal boron nitride, such as monolayer hexagonal boron nitride or multi-layered hexagonal boron nitride.

[0272] Example 9: The device of any examples herein, particularly examples 1-8, wherein the second insulating layer comprises hexagonal boron nitride, such as monolayer hexagonal boron nitride or multi-layered hexagonal boron nitride.

[0273] Example 10: The device of any examples herein, particularly examples 1-9, wherein the first insulating layer has an average thickness of from 1 nanometer to 5 nanometers, such as from 1.5 nm to 3.5 nm or from 1 to 3 nm.

[0274] Example 11 : The device of any examples herein, particularly examples 1-10, wherein the second insulating layer has an average thickness of from 1 nanometer to 5 nanometers, such as from 1.5 nm to 3.5 nm or from 1 to 3 nm.

[0275] Example 12: The device of any examples herein, particularly examples 1-11, wherein the first insulating layer and the second insulating layer are substantially the same.

[0276] Example 13: The device of any examples herein, particularly examples 1-11, wherein the first insulating layer and the second insulating layer are different.

[0277] Example 14: The device of any examples herein, particularly examples 1-13, wherein the first insulating layer and the second insulating layer together have a total average thickness of from 2 to 10 nanometers, such as from 3 to 7 nm or from 4 to 6 nanometers.

[0278] Example 15: The device of any examples herein, particularly examples 1-14, wherein the impurity comprises a defect, such as a vacancy, an interstitial defect, a dopant, or a combination thereof. Example 16: The device of any examples herein, particularly examples 1-15, wherein the impurity comprises a metal atom, such as a metal selected from the group consisting of Er, Mn, Pt, Fe, V, Cu, Co, Yb, Pr, Eu, and combinations thereof.

[0279] Example 17: The device of any examples herein, particularly examples 1-16, wherein the impurity comprises a molecule, such as a macrocyclic ligand.

[0280] Example 18: The device of any examples herein, particularly examples 1-17, wherein the impurity comprises a molecule, such as a porphyrin, a corrole, a phthalocyanine, or a combination thereof.

[0281] Example 19: The device of any examples herein, particularly examples 1-18, wherein the molecule comprises a metal-ligand molecule, such as a metal porphyrin, a metal corrole, a metal phthalocyanine, or a combination thereof.

[0282] Example 20: The device of any examples herein, particularly example 19, wherein the metal comprises Cu, V, Co, Fe, Mn, Zn, Ni, Cr, Ti, or a combination thereof.

[0283] Example 21 : The device of any examples herein, particularly examples 1-20, wherein the impurity comprises a molecule, such as copper phthalocyanine, vandyl phthalocyanine, or a combination thereof.

[0284] Example 22: The device of any examples herein, particularly examples 1-21, wherein the impurity comprises a molecule, such as one or more of those shown in Figure 4.

[0285] Example 23: The device of any examples herein, particularly examples 1-22, wherein the impurity comprises a third two-dimensional material, optionally further comprising a defect therein.

[0286] Example 24: The device of any examples herein, particularly examples 1-23, wherein the device further comprises a first electrode disposed on and in electrical and physical contact with at least a portion of the first conductive layer.

[0287] Example 25: The device of any examples herein, particularly example 24, wherein the first electrode comprises a metal, such as gold, and / or a magnetic material.

[0288] Example 26: The device of any examples herein, particularly examples 1-25, wherein the device further comprises a second electrode disposed on and in electrical and physical contact with at least a portion of the second conductive layer.

[0289] Example 27: The device of any examples herein, particularly example 26, wherein the second electrode comprises a metal, such as gold, and / or a magnetic material.

[0290] Example 28: The device of any examples herein, particularly examples 1-27, wherein the tunnel junction device is a qubit. Example 29: A method of making the device of any examples herein, particularly examples 1-28.

[0291] Example 30: The method of any examples herein, particularly example 29, wherein the method comprises, in any order: disposing the first insulating layer on at least a portion of the first conductive layer; disposing the impurity on the first insulating layer or the second insulating layer; disposing at least a portion of the first insulating layer on at least a portion of the second insulating layer to substantially encapsulate the impurity; disposing the second insulating layer on at least a portion of the first insulating layer; and disposing the second conductive layer on at least a portion of the second insulating layer.

[0292] Example 31 : The method of any examples herein, particularly example 30, wherein disposing the first conductive layer, the first insulating layer, the second insulating layer, the second conductive layer, or a combination thereof comprises mechanical exfoliation and / or dry transfer.

[0293] Example 32: The method of any examples herein, particularly example 30 or example 31, wherein disposing the impurity comprises drop casting, spin casting, evaporation, or a combination thereof.

[0294] Example 33: An article of manufacture comprising the device of any examples herein, particularly examples 1-28.

[0295] Example 34: The article of any examples herein, particularly example 33, wherein the article comprises a quantum device, such as a quantum information system, a quantum computing device, a quantum sensor, a quantum transduction device, or a combination thereof.

[0296] Example 35: A method of use of the device of any examples herein, particularly examples 1-28.

[0297] Example 36: The method of any examples herein, particularly example 35, wherein the method comprises using the device in a quantum device, such as a quantum information system, a quantum computing device, a quantum sensor, a quantum transduction device, or a combination thereof.

[0298] Example 37: The method of any examples herein, particularly example 35, wherein the method comprises using the device to characterize the impurity.

[0299] Example 38: The method of any examples herein, particularly example 37, wherein the method comprises using ESR (e.g., pulsed ESR) to characterize the impurity.

[0300] Other advantages which are obvious and which are inherent to the invention will be evident to one skilled in the art. It will be understood that certain features and sub-combinations are of utility and may be employed without reference to other features and sub-combinations. This is contemplated by and is within the scope of the claims. Since many possible embodiments may be made of the invention without departing from the scope thereof, it is to be understood that all matter herein set forth or shown in the accompanying drawings is to be interpreted as illustrative and not in a limiting sense.

[0301] The compositions, devices, and methods of the appended claims are not limited in scope by the specific methods described herein, which are intended as illustrations of a few aspects of the claims and any methods that are functionally equivalent are intended to fall within the scope of the claims. Various modifications of the compositions, devices, and methods in addition to those shown and described herein are intended to fall within the scope of the appended claims.

[0302] Further, while only certain representative method steps disclosed herein are specifically described, other combinations of the method steps also are intended to fall within the scope of the appended claims, even if not specifically recited. Thus, a combination of steps, elements, components, or constituents may be explicitly mentioned herein or less, however, other combinations of steps, elements, components, and constituents are included, even though not explicitly stated.

Claims

CLAIMSWhat is claimed is:

1. A modular design for a zero-dimensional (OD) state tunnel junction device comprising: a first conductive layer; a first insulating layer disposed on and in electrical and physical contact with at least a portion of the first conductive layer, the first insulating layer comprising a first two-dimensional material; a second insulating layer disposed on and in electrical and physical contact with at least a portion of the first insulating layer, such that at least a portion of the first insulating layer is sandwiched between at least a portion of the second insulating layer and at least a portion of the first conductive layer, the second insulating layer comprising a second two-dimensional (2D) material; an impurity sandwiched between and substantially encapsulated by the first insulating layer and the second insulating layer, the impurity being in electrical and physical contact with at least a portion of both the first insulating layer and the second insulating layer, the impurity comprising a defect, an atom, a molecule, or a combination thereof, wherein the impurity is a zero-dimensional (OD) system; and a second conductive layer disposed on and in electrical and physical contact with at least a portion of the second insulating layer, such that at least a portion of the second insulating layer is sandwiched between at least a portion of the first insulating layer and at least a portion of the first conductive layer.

2. The device of claim 1, wherein the first conductive layer comprises a two-dimensional material.

3. The device of claim 1 or claim 2, wherein the second conductive layer comprises a two- dimensional material.

4. The device of any one of claims 1-3, wherein the first conductive layer comprises graphene, such as monolayer graphene or multi-layered graphene.

5. The device of any one of claims 1-4, wherein the second conductive layer comprises graphene, such as monolayer graphene or multi-layered graphene.

6. The device of any one of claims 1-5, wherein the first conductive layer and the second conductive layer are substantially the same.

7. The device of any one of claims 1-5, wherein the first conductive layer and the second conductive layer are different.

8. The device of any one of claims 1-7, wherein the first insulating layer comprises hexagonal boron nitride, such as monolayer hexagonal boron nitride or multi-layered hexagonal boron nitride.

9. The device of any one of claims 1-8, wherein the second insulating layer comprises hexagonal boron nitride, such as monolayer hexagonal boron nitride or multi-layered hexagonal boron nitride.

10. The device of any one of claims 1-9, wherein the first insulating layer has an average thickness of from 1 nanometer to 5 nanometers, such as from 1.5 nm to 3.5 nm or from 1 to 3 nm.

11. The device of any one of claims 1-10, wherein the second insulating layer has an average thickness of from 1 nanometer to 5 nanometers, such as from 1.5 nm to 3.5 nm or from 1 to 3 nm.

12. The device of any one of claims 1-11, wherein the first insulating layer and the second insulating layer are substantially the same.

13. The device of any one of claims 1-11, wherein the first insulating layer and the second insulating layer are different.

14. The device of any one of claims 1-13, wherein the first insulating layer and the second insulating layer together have a total average thickness of from 2 to 10 nanometers, such as from 3 to 7 nm or from 4 to 6 nanometers.

15. The device of any one of claims 1-14, wherein the impurity comprises a defect, such as a vacancy, an interstitial defect, a dopant, or a combination thereof.

16. The device of any one of claims 1-15, wherein the impurity comprises a metal atom, such as a metal selected from the group consisting of Er, Mn, Pt, Fe, V, Cu, Co, Yb, Pr, Eu, and combinations thereof.

17. The device of any one of claims 1-16, wherein the impurity comprises a molecule, such as a macrocyclic ligand.

18. The device of any one of claims 1-17, wherein the impurity comprises a molecule, such as a porphyrin, a corrole, a phthalocyanine, or a combination thereof.

19. The device of any one of claims 1-18, wherein the molecule comprises a metal -ligand molecule, such as a metal porphyrin, a metal corrole, a metal phthalocyanine, or a combination thereof.

20. The device of claim 19, wherein the metal comprises Cu, V, Co, Fe, Mn, Zn, Ni, Cr, Ti, or a combination thereof.

21. The device of any one of claims 1-20, wherein the impurity comprises a molecule, such as copper phthalocyanine, vandyl phthalocyanine, or a combination thereof.

22. The device of any one of claims 1-21, wherein the impurity comprises a molecule, such as one or more of those shown in Figure 4.

23. The device of any one of claims 1-22, wherein the impurity comprises a third two- dimensional material, optionally further comprising a defect therein.

24. The device of any one of claims 1-23, wherein the device further comprises a first electrode disposed on and in electrical and physical contact with at least a portion of the first conductive layer.

25. The device of claim 24, wherein the first electrode comprises a metal, such as gold, and / or a magnetic material.

26. The device of any one of claims 1-25, wherein the device further comprises a second electrode disposed on and in electrical and physical contact with at least a portion of the second conductive layer.

27. The device of claim 26, wherein the second electrode comprises a metal, such as gold, and / or a magnetic material.

28. The device of any one of claims 1-27, wherein the tunnel junction device is a qubit.

29. A method of making the device of any one of claims 1-28.

30. The method of claim 29, wherein the method comprises, in any order: disposing the first insulating layer on at least a portion of the first conductive layer;disposing the impurity on the first insulating layer or the second insulating layer; disposing at least a portion of the first insulating layer on at least a portion of the second insulating layer to substantially encapsulate the impurity; disposing the second insulating layer on at least a portion of the first insulating layer; and disposing the second conductive layer on at least a portion of the second insulating layer.

31. The method of claim 30, wherein disposing the first conductive layer, the first insulating layer, the second insulating layer, the second conductive layer, or a combination thereof comprises mechanical exfoliation and / or dry transfer.

32. The method of claim 30 or claim 31, wherein disposing the impurity comprises drop casting, spin casting, evaporation, or a combination thereof.

33. An article of manufacture comprising the device of any one of claims 1-28.

34. The article of claim 33, wherein the article comprises a quantum device, such as a quantum information system, a quantum computing device, a quantum sensor, a quantum transduction device, or a combination thereof.

35. A method of use of the device of any one of claims 1-28.

36. The method of claim 35, wherein the method comprises using the device in a quantum device, such as a quantum information system, a quantum computing device, a quantum sensor, a quantum transduction device, or a combination thereof.

37. The method of claim 35, wherein the method comprises using the device to characterize the impurity.

38. The method of claim 37, wherein the method comprises using ESR (e.g., pulsed ESR) to characterize the impurity.

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