Manufacturing method for quantum moirÉ interfaces

Abstract

Example embodiments relate to scalable, in situ, streamlined manufacturing methods for generating macroscopic moiré interfaces using two-dimensional van der Waals materials. For instance, provided at least one bulk material, example methods include selective engineered monolayer exfoliation of two different monolayers, controlled twist of one exposed monolayer with respect to the other monolayer, and subsequent coupling in a face to face assembly, so as to form macroscopic quantum moiré bilayers. In certain embodiments, macroscopic heterostructure moiré interfaces can be assembled using this tunable manufacturing method to generate one or more new properties that do not exist in isolation. Furthermore, a device may be formed that includes a substrate, an active layer made from a macroscopic quantum moiré bilayer and two or more terminals, allowing for the unique properties of the macroscopic quantum moiré bilayer to be utilized for device applications.

Description

Manufacturing Method for Quantum Moire InterfacesCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application is a non-provisional patent application claiming priority to US Provisional Patent Application No. 63 / 660,802 filed on June 17, 2024, the contents of which are hereby incorporated by reference.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with Government support under contract HR0011-23-9-0108 awarded by the Defense Advanced Research Projects Agency, under contract DE-AC02-76SF00515 awarded by the Department of Energy, and under contract 2026822 awarded by the National Science Foundation. The Government has certain rights in the invention.BACKGROUND

[0003] Moire superlattices arise from interference at the interface between two crystal lattice planes differing in lattice constants and / or alignment angles. They have recently emerged as an intriguing research area in condensed matter physics. At specific twist angles (i.e. magic angles) of a van der Waals (vdW) bilayer interface, these superlattices substantially reduce electron kinetic energy, allowing Coulomb interactions to predominate, fostering strong electron correlations, resulting in flat electronic bands near the Fermi level. With tunable bandfilling and doping conditions, moire superlattices have become a versatile platform to study the collective behavior of electrons, excitons, solitons, and topological band structures. In addition to bilayers, other experimental developments have been undergoing to explore moire systems in mixed dimensional systems, with more robust superconductivity and richer excitonic physics. For example, the first demonstration of Van Hove singularities at magic angles was demonstrated for twisted graphene / graphite structure. Recent transport measurements on graphene / graphite systems show formation of a single quasi-two-dimensional hybrid structure through a combination of gate-tunable moire potential and graphite surface states, in which the properties of a bulk crystal are shown to be tuned by a superlattice potential occurring at the interface.

[0004] Twisted bilayer moire structures represent a versatile quantum material platform for superconducting and quantum processing devices (twistronic devices). Current preparation methods are laborious, produce micrometer sample size, and are rife with key challenges such as extremely low production yield, efficiency, and reproducibility, with significant inhomogeneity and interfacial contamination. These challenges prevent the mass production and manufacturing of twistronic devices.

[0005] Achieving the exotic correlated electronic phases in a moire structure demands very precise control of the rotational alignment between atomically thin layers, requiring angular precisions of less than 0.1 degrees. vdW twisted structures have been realized with the tear-and-stack method using micron-sized flakes. However, reproducible fabrication of uniform moire systems, particularly across macroscopic areas, remains a formidable challenge. The limitations encompass a broad spectrum of factors, including the uniformity of twist angles and strains, contamination-induced interfacial disorders, lattice relaxation / reconstruction and the tendency of untwisting at high processing temperatures. Traditional “Scotch tape” exfoliation techniques are inherently stochastic, producing samples ranging from a few micrometers to tens of micrometers in size, limiting the area of the twisted moire interfaces. Moreover, these techniques often expose the monolayer to polymer and / or substrate surface prior to stacking, inevitably resulting in interfacial contaminations and bubbles that may weaken the bilayer interaction. As a result, the efficiency and reproducibility of current tear-and-stack assembly methods is notably low. Furthermore, the conventional Scotch tape technique is time and labor intensive, not amenable to rapid prototyping or manufacturing optimization, and poorly scalable. On the other hand, advanced growth techniques, such as chemical vapor deposition (CVD) or physical epitaxy, have been used to achieve direct synthesis of 2D monolayers over wafer scale. However, although recent advances have been made on growing microscopic bilayer flakes with different twist angles, the precise manipulation of large-area twisted structures at controlled angles, particularly near the magic angle, remains elusive. Due to the challenges above in scalability and mass production, high-quality moire structures are currently “more like an art piece” than scalable product. To harness the full potential of moire materials, more optimized fabrication processes to ensure reproducibility, stability, and applicability across macroscopic areas are desired.SUMMARY

[0006] The present disclosure describes methods and systems capable of producing moire superlattices from a wide range of 2D materials with unprecedented uniformity and versatility. These methods and systems produce highly uniform moire superlattices at vdW interfaces of twisted monolayer on bulk systems as well as twisted bilayer systems, achieving high throughput and near-unity yield over centimeter-scale macroscopic areas. Methods and systems described herein beneficially permit the macroscopic exploration of moire physics with spectroscopic tools that were previously limited by their spatial resolution. Furthermore, the macroscopic dimension will significantly enhance the thermal stability of the small twist angle structures, rendering them more robust against untwisting under high-temperature annealing processes.

[0007] In contrast to prevailing manufacturing methods, which rely on stochastic processes, the present approach ensures a deterministic process. Additional advantages include the capability to manufacture sizes ranging from millimeters to centimeters, constrained only by van der Waals bulk crystal size. The present disclosure also enables unprecedented manufacturing speed and uniformity over large length scales (mm to cm), in contrast to current methods that often yields a substantial level of moire lattice disorder. The disclosed methods achieve near-perfect yield, whereas current methods have not and may only produce very localized areas exhibiting moire patterns. Furthermore, methods and systems disclosed herein ensure superb interface cleanliness, addressing the common issue of interfacial contaminations in current techniques. Additionally, such methods facilitate batch assembly for mass production.

[0008] In an aspect, a method of manufacturing is provided. The method of manufacturing includes providing a first substrate, such as a layered bulk crystal. The first substrate includes a plurality of two-dimensional monolayers. The plurality of two-dimensional monolayers includes a first exposed monolayer. The method also includes pressing a first metal surface, supported by a polymer backing, onto the first substrate by way of the first exposed monolayer. The method additionally includes removing the first metal surface from the first substrate and thereby exfoliating the first exposed monolayer from a remaining monolayer stack. Furthermore the method includes providing a second substrate, such as a layered bulk crystal. The second substrate includes a plurality of two-dimensional monolayers. The plurality of two-dimensional monolayers includes a second exposed monolayer. The method also includes pressing a second metal surface, supported by a different polymer backing, onto thesecond substrate by way of the second exposed monolayer and removing the second metal surface from the second substrate and thereby exfoliating the second exposed monolayer from a remaining monolayer stack. The method yet further includes rotating the first exposed monolayer with respect to the second exposed monolayer. The method also includes coupling the first exposed monolayer to the second exposed monolayer in a face-to-face assembly so as to form a twisted bilayer. The polymer backing for the first monolayer and the second monolayer have different releasing conditions, allowing them to be released and cleaned subsequently to enable clean bilayer structures that can be transferred onto any destination substrate.

[0009] In another aspect, an additional method of manufacturing is provided. The method of manufacturing includes providing a substrate, such as a layered bulk crystal. The substrate includes a plurality of two-dimensional monolayers. The plurality of two-dimensional monolayers includes an exposed monolayer. The method also includes pressing a metal surface, supported by a polymer backing, onto the substrate by way of the exposed monolayer. The method additionally includes removing the metal surface from the substrate and thereby exfoliating the exposed monolayer from a remaining monolayer stack. The method yet further includes rotating the exposed monolayer with respect to the remaining monolayer stack or a new monolayer stack. The method also includes pressing the exposed monolayer onto the monolayer stack, so as to form a twisted monolayer on bulk structure. The metal surface supported by a polymer backing is cleaned through a combination of dissolution and etching processes.

[0010] Other aspects are possible and contemplated within the context of the present disclosure.BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 is a schematic of the fabrication process for macroscopic morie structures, according to an example embodiment.

[0012] Figure 2 illustrates uniform moire superlattices over macroscopic length scales, according to an example embodiment.

[0013] Figure 3 illustrates additional uniform moire structures over macroscopic length scales, according to an example embodiment.

[0014] Figure 4 illustrates TFM / PFM images of different monolayer-on bulk moire structures, according to an example embodiment.

[0015] Figure 5 illustrates photographs of different macroscopic monolayer on bulk moire superlattices, according to an example embodiment.

[0016] Figure 6 illustrates lateral piezoresponse force microscopy of larger area scans of 1.16° twisted WS2 / WS2, according to an example embodiment.

[0017] Figure 7 illustrates lateral piezoresponse force microscopy of a freshly cleaved WS2 crystal, as a control experiment for comparison, according to an example embodiment.

[0018] Figure 8 illustrates PFM images of twisted bilayers on different substrates according to an example embodiment.

[0019] Figure 9 illustrates twisted moire structures with different materials, according to an example embodiment.

[0020] Figure 10 illustrates additional large-area PFM scans of twisted WSe2 on bulk M0S2 at varying magnifications according to an example embodiment.

[0021] Figure 11 illustrates PFM images of twisted M0S2 moire structures fabricated using different approaches, and LEED diffraction patterns of a M0S2 sample, illustrating the superior thermal stability of the macroscopic moire structures, according to an example embodiment.

[0022] Figure 12 illustrates reciprocal space characterization of moire superlattices, according to an example embodiment.

[0023] Figure 13 illustrates band dispersion diagrams and model fitting information, according to an example embodiment.

[0024] Figure 14 illustrates a simulation of ARPES on twisted M0S2 moire structure and constant energy contour (CEC) diagrams, according to an example embodiment.

[0025] Figure 15 illustrates high-resolution ARPES spectra, according to an example embodiment.

[0026] Figure 16 illustrates experimental LEED patterns and the corresponding reciprocal space simulation as well as a schematic of a reconstructed superlattice according to an example embodiment.

[0027] Figure 17 illustrates LEED diffraction intensities of the monolayer and moire spots of 7eMoS2 / MoS2as a function of electron energy, according to an example embodiment.

[0028] Figure 18 illustrates photoluminescence spectra of gold exfoliated monolayers according to an example embodiment.

[0029] Figure 19 illustrates a diagram of a method, according to an example embodiment.

[0030] Figure 20 illustrates a diagram of a method, according to an example embodiment.DETAILED DESCRIPTIONOverview

[0031] Moire superlattices, engineered through precise stacking of van der Waals (vdW) layers, hold immense promise for exploring strongly correlated and topological phenomena. A primary challenge lies in the most commonly-used preparation method: tearand-stack of Scotch tape exfoliated monolayers. That method has low efficiency and reproducibility, along with challenges of twist angle inhomogeneity, interfacial contaminations, micrometer sizes, and a tendency to untwist at elevated temperatures. Here, methods and systems are described to enable construction of mixed-dimensional and twisted bilayer vdW moire structures at high production speed, near-unity yield, with pristine interfaces, precisely controlled twist angles, establishing highly consistent moire superlattices over macroscopic scale (up to centimeters), and with enhanced thermal stability. Present embodiments demonstrate versatility across various vdW materials including transition metal dichalcogenides (TMDC), graphene, and hexagonal boron nitride (hBN). The reciprocal space back-folded lattice and moire mini band structures are evaluated with low energy electron diffraction (LEED) and angle-resolved photoemission spectroscopy (ARPES). Methods and systems described herein will have broad applications in both fundamental studies and mass production of twistronic devices.

[0032] The presently described methods and systems beneficially leverage a unique engineering technique of moire superlattices from a wide range of 2D materials with unprecedented uniformity and versatility. This technique produces highly uniform moire superlattices at the vdW interface of twisted monolayer on bulk systems, achieving high throughput and near-unity yield over centimeter scale macroscopic areas. Such materials permit the macroscopic exploration of moire physics with spectroscopic tools that were previously limited by their spatial resolution. Furthermore, the macroscopic dimension will significantly enhance the thermal stability of the small twist angle structures, rendering them more robust against untwisting under high-temperature annealing processes.

[0033] Methods described herein provide an in situ batch assembly manufacturing technique that dramatically increases the rate of sample manufacturing. Furthermore, thedescribed methods of manufacture are compatible with rapid prototyping and manufacturing optimization efforts.

[0034] Figure 1 is a schematic diagram 100 illustrating the construction of macroscopic moire structures, according to example embodiments. As depicted in Figure 1, an example embodiment includes the utilization of a fresh and clean gold surface template-stripped from a plasma-cleaned silicon substrate. The gold surface has strong adhesion with a variety of vdW monolayers, which offers the opportunity to disassemble van der Waals bulk crystals layer-by-layer into macroscopic monolayers. To start the exfoliation, the template-stripped gold layer, backed with thermal-release tape (TRT) and polyvinylpyrrolidone (PVP) (Figure 1A), is stamped onto a freshly cleaved vdW crystal (Figures IB and 1C). Lifting the gold tape exfoliates a monolayer from the vdW crystal (Figure ID), which is subsequently rotated to a target angle (Figure IE, inset a) and stacked back onto the same vdW crystal (Figure IE, inset b) to create a homo-twist system. As a result, the twisted vdW interface is created directly at the pristine vdW interface between the freshly cleaved monolayer and the freshly cleaved crystal surface (Figure IE, inset b). This swift in situ process effectively addresses the interfacial contamination challenges inherent in traditional method of stacking previously deposited monolayers, encompassing contaminations from polymers, solvents, and substrates during stacking. After assembly, the TRT, PVP, and Au components are meticulously removed through a sequence of thermal treatment, solvent rinsing, and etching with KI / E solution, respectively (Figure IE, inset c), ensuring a clean top surface in the final moire structure. Benefiting from perfect lattice alignment of exfoliated monolayer within the original vdW layered crystal, the target twist angle in homo twisted moire structures can be precisely controlled, either manually or through automated processes. This in situ procedure is facile with high yield, representing a significant improvement compared to conventional techniques, which are laborious with limited scalability and low yield.

[0035] For twisted bilayer moire structures, a complementary protocol may be employed in which two exfoliated monolayers — each freshly cleaved from bulk — are assembled face-to face with controlled angular alignment. In this example embodiment, one monolayer is supported by a 50 nm Au film backed with TRT and PVP, while the other is be supported by a 150 nm Au film backed with a polycarbonate (PC) layer on PDMS, resulting in a TRT / PVP / 50 nm Au / twisted-bilayer / 150 nm Au / PC / PDMS stack (Figure IF, inset a). Other layer thicknesses and materials are contemplated and possible. These polymer layers may be specifically chosen for their contrasting hydrophobicity, which facilitates selective removal after assembly. The top TRT, PVP and Au layers are removed sequentially via thermal release,water rinsing, and KI / I2 etching for a controlled duration of 15-20 seconds, analogous to that used for monolayer-on-bulk structures (Figure IF, inset c). The structure is then flipped and transferred onto the target substrate (SiC>2 / Si) (Figure IF, inset d). Heating to 180 °C releases the PDMS and softens the PC, allowing the bilayer to conform and adhere to the substrate. Finally, the PC is dissolved in chloroform and cleaned with O2 plasma, and the gold layer is removed via KI / L wet etching, completing the fabrication of the twisted bilayer moire structure (Figure IF, inset e).

[0036] The target twist angle in the presently disclosed moire assemblies can be controlled with high precision — either manually or via automated alignment routines. The exfoliation-twist-stacking process may be completed within seconds and involves minimal environmental exposure, enabling the in situ formation of a twisted vdW interface between two freshly cleaved, pristine crystal surfaces. This rapid and deterministic approach effectively overcomes the interfacial contamination issues that are commonly encountered in conventional methods, which often involve exposure of monolayer surfaces to polymers, solvents, and substrates during sample preparation. While the process shown here in example embodiments is completed with a hand-operated mechanical stage, it can be readily adaptable to the robotic stacking machines for scalability.

[0037] Figure 2 illustrates uniform morie superlattices over macroscopic length scales 200, according to an example embodiment. This in situ procedure is facile with near-unity exfoliation and stacking efficiency. Both a twisted M0S2 monolayer / bulk M0S2 structure and a twisted bilayer M0S2 structure are shown, each with macroscopic scale dimensions. The surface of the resulting macroscopic moire structure is exceptionally flat and free of interfacial bubbles, as evidenced by the atomic force microscopy (AFM) image in Figure 2, inset b, demonstrating a root mean square (RMS) roughness of 320 pm. This high degree of cleanliness and flatness arises from the fact that the twisted vdW interface is formed directly between the freshly cleaved pristine surfaces.

[0038] To demonstrate the uniformity of the twist angle and the resulting moire structures real space images of the moire structures may be obtained using piezoresponse force microscopy (PFM) or torsional force microscopy (TFM). In this example embodiment, PFM images are generated at 22 random locations spaced millimeters apart across a centimeter-scale surface, all under identical operating conditions (see Figure 2, inset d). The scale bar in Figure 2, inset d indicates 50 nm. The high-quality PFM images demonstrate exceptional uniformity of the moire superlattice across the entire area. From the real-space periodicity of the moire fringes, the local twist angles at each location were quantitatively extracted. Remarkably, thestandard deviation of the twist angle across the 22 sampled spots is only 0.05°, indicating that the moire pattern remains highly consistent over millimeter-to-centimeter length scales.

[0039] In this example embodiment, reciprocal-space imaging of the macroscopic moire lattice was also performed using low-energy electron diffraction (LEED), a conventional surface-sensitive technique capable of probing large areas with electron beam spot sizes up to ~1 mm2. The LEED pattern of a 6° twisted M0S2 monolayer on bulk M0S2 acquired at 142.3 eV electron energy is shown in Figure 2, inset e. The LEED pattern of a 3° twisted M0S2 bilayer acquired at 107 eV electron energy is presented in Figure 2, inset f. In both cases, in addition to the primary Bragg reflections from the monolayer and / or bulk lattices, clear satellite peaks corresponding to the moire superlattice are observed.

[0040] These moire satellite peaks arise from picometer-scale periodic lattice distortions (PLDs), which frequently occur at small angles twisted vdW systems. PLDs involve both in-plane and out-of-plane lattice modulations, leading to alternating AB and BA stacking domains separated by soliton-like shear boundaries. This structural relaxation reduces the local lattice symmetry and minimizes the total free energy, shaping the miniband structures, inducing gap openings and defining band topologies, with direct consequences for the emergent quantum phenomena such as charge density waves (CDWs), fractional quantum anomalous Hall effects, and other strongly correlated behaviors. The long- wavelength lattice reconstructions act as a phase grating for scattered electrons. As a result, the reciprocal lattice observed in LEED is not a simple superposition of the two layers, but instead features additional satellite peaks defining a moire mini-Brillouin zone.

[0041] The observation of well-defined moire satellite peaks in LEED, despite the macroscopic size of the probe beam, confirms the long-range structural uniformity of the PLD-modulated moire lattice over millimeter length scales. Furthermore, the twist angles extracted from LEED are in excellent agreement with those obtained from real-space measurements using PFM. A detailed LEED peak profile analysis of the twisted M0S2 monolayer / bulk structure is shown in Figure 2, inset g. The diffraction peaks, which are clearly resolved and within the linear dynamic range of the detector, were fitted using Lorentzian functions. The full width at half maximum (FWHM) of the monolayer peak differs from that of the bulk by only 0.5 pixels, which is nearly identical to the fitting uncertainty of 0.4 pixels (corresponding to -0.14°), indicating that the monolayer FWHM is statistically indistinguishable from the bulk at 95% confidence interval within experimental uncertainty. The minimal broadening confirms that the in situ exfoliation and stacking process introduces negligible angular disorder, evenacross millimeter scale regions, and the orientation of monolayer lattice remains highly uniform and well-matched to the consistency of the bulk crystal surface.

[0042] Figure 3 shows additional TFM measurements on a different M0S2 / b-MoS? moire superlattice on Si sample 300, demonstrating a similar high degree of uniformity across macroscopic areas, confirming the robustness and repeatability of the fabrication process. The scale bar in the lateral piezoresponse force microscopy (LPFM) images on the right corresponds to 25 nm. The moire structures exhibit clear responses in both vertical and lateral PFM modes

[0043] Figure 4 illustrates TFM / PFM images of different monolayer-on bulk moire structures 400, according to an example embodiment. This demonstrates that this method allows for effective creation of highly customizable twisted vdW interfaces across a diverse range of vdW materials. In addition to homo-twisted TMDC systems, combining a freshly exfoliated monolayer and another freshly cleaved vdW crystal leads to the production of twisted vdW heterostructures with similar uniformity over extended areas. A few examples of these moire structures, including WSe2 / MoSe2, WSe2 / WS2, and WSe2 / MoS2, are shown in Figure 4, insets g-i.

[0044] Figure 5 illustrates different macroscopic monolayer on bulk moire superlattices 500, according to an example embodiment. Here, photographs are shown for a variety of monolayer on bulk moire superlattices, demonstrating the use of this method on a variety of different materials for both homo-structures (insets a-f) and hetero-structures (insets g-i).

[0045] Figure 6 illustrates lateral piezoresponse force microscopy of larger area scans of 1.16° twisted WS2 / WS2 600, according to an example embodiment. Here the scale bar corresponds to 200 nm. Figure 6, inset a shows the amplitude, Figure 6 inset b shows the phase, and Figure 6 inset c shows the topography.

[0046] Figure 7 illustrates lateral piezoresponse force microscopy of freshly cleaved WS2 crystal 700, as a control experiment for comparison, according to an example embodiment. Here the scale bar corresponds to 200 nm. Figure 7, inset a shows the topography, Figure 7, inset b shows the amplitude of the LPFM micrograph, and Figure 7, inset c shows the phase signal of the LPFM micrograph showing a background with no moire structure. This analysis reveals the exceptional cleanliness of the surface post-cleaving, offering insight the highly uniform nature of the moire superlattice over large length scales.

[0047] Figure 8 illustrates PFM images of twisted bilayers on different substrates according to an example embodiment 800. Figure 8, inset a shows a 1.2° twisted bilayer of M0S2 prepared on highly oriented pyrolytic graphite (HOPG). Figure 8, inset b shows a 1.8°twisted bilayer of WS2 prepared on p-doped Si. Here it can be seen that the quality of PFM images is affected by the uniformity of the substrate.

[0048] Figure 9 illustrates additional material systems for twisted moire structures 900. By using this method on a variety of material systems, the physics of spin, topology, and anisotropy can be further explored. Here, example images are shown for MoSe2 / ReS2, MoSe2 / WTe2, and MoSe2 / MoTe2. The scale bar corresponds to 50 nm.

[0049] Figure 10 illustrates additional large-area lateral PFM amplitude scans of a 1.98° twisted WSe2 / b-MoS2 sample 1000. The scale bar of the top image is 500nm, whereas the scale bars for the bottom three images are 50 nm, 50nm, and 5 nm from left to right. Despite the nanometer moire lattice period at this twist angle, the fine features remain clearly visible even at the micrometer scale.

[0050] At elevated temperatures, twisted van der Waals (vdW) interfaces, especially those at small angles near magic angle, tend to change twist angles. Thermodynamically, moire structures at small angles may revert from an incommensurate state to a commensurate zerodegree stacking, which is the most stable configuration. In practice, however, pinning of the defects and disordered interfacial contaminations may lead to random variation in local twist angle during thermal annealing. This instability presents a significant challenge for the reproducibility of moire physics experiments and for the development of twistronic devices, as the final twist angle often deviates from the initial fabrication design. Moreover, the thermal relaxation pathway often navigates through multiple potential energy barriers, encountering several locally stable energy states from the varying degrees of commensurability among atomic stackings across the twisted interface. Both the energy barrier and the number of locally stable energy states scale with the flake sizes. Therefore, larger flakes with clean vdW interfaces will likely offer enhanced thermal stabilities.

[0051] Figure 11 illustrates the temperature stability of vdW interfaces made using different methods 1100 in an example embodiment. Two moire structures with similar small twist angles were prepared: a micrometer scale M0S2 bilayer with twist angle of 1.78° fabricated using traditional scotch tape exfoliation and tear and stack method, and a macroscopic M0S2 moire structure with twist angle of 1.15° prepared using the deterministic approach of the present disclosure. PFM images of these samples both before and after annealing are shown in Figure 11, inset a, with a scale bar of 50 nm. Compared with the macroscopic sample, the PFM image of microscopic sample shows noticeable inhomogeneity, which is common in traditional tear and stack method. Upon annealing at 200 °C for a couple of hours, the twist angle of the microscopic moire structure is increased by ~0.3 degrees, likelydue to pinning at a nearby defect or contamination site. In contrast, the macroscopic moire structure exhibits a much smaller change in twist angle, which decreases by only ~ 0.05 degrees, despite starting with a smaller initial twist angle. Further increasing the anneal temperature produces similar contrast, demonstrating the macroscopic moire structures present a higher degree of thermal stability. The thermal stability of the macroscopic structures was further tested by annealing a 6° twisted M0S2 sample to elevated temperature (500 °C) for over an hour. The LEED patterns before and after the anneal process, shown in Figure 11, inset b, demonstrate identical twist angles before and after the high temperature treatment. This enhanced stability represents a key advantage for achieving high reproducibility in future large-scale processing and device manufacturing.

[0052] In long periodic moire superlattices, the introduction of a slowly varying periodic potential leads to the formation of mini-Brillouin zones (BZs) and corresponding back-folded replicas of the electronic band structure. The replicas from the states at the BZ corner, and their associated bandgap openings, topological characteristics, and flat band formation under the displacement field play a central role in the emergence of the unique quantum phases. However, precise theoretical modeling of moire minibands with spin valley textures remains computationally demanding due to the large size of moire unit cell. As such, direct experimental measurements, such as angle resolved photoemission spectroscopy (ARPES), are essential for probing the electronic structure of moire minibands in twisted TMDC systems modified by the many-body interactions.

[0053] In TMDC monolayers, the valence band maximum lies at the K point of BZ with spin valley polarizations. The backfolded band structures at the valence band edge are particularly important in determining the physical properties under integer or fractional hole fillings. However, despite the critical importance of K valley, experimental observations of back-folded moire minibands in twisted TMDC systems have so far been only limited to the point instead. This is in part due to the constraints imposed by small sample sizes, which necessitated the use of ARPES systems with micrometer- or nanometer-scale spatial resolution. The TMDC bands at point exhibit inherently much stronger photoemission cross section and participate in interlayer coupling due to their out-of-plane orbital make-up, whereas the bands around K valleys are predominantly derived in-plane Mo tZ-orbitals, which exhibits weaker out of plane interlayer hybridization and lower photoemission intensity. Consequently, detecting moire minibands at the K-point is substantially more challenging. Such detection demands both high interfacial quality and high-throughput measurement capabilities — requirements that arenow becoming feasible with the emergence of large-area, uniform moire samples and the application of conventional high-resolution, high throughput ARPES systems.

[0054] Figure 12 illustrates reciprocal space characterization of moire superlattices 1200, according to an example embodiment. Here, the back-folded miniband replicas in the moire mini -Brillouin zone are observed not only at the point, but also at the K-point of twisted monolayer MoS2 / bulk M0S2 using conventional high resolution ARPES with large beam spot sizes. Figure 12, inset a presents the measured electronic dispersion along the -K high-symmetry line in a 4.5e twisted monolayer MoS2 / bulk M0S2 structure. The satellite bands around both the - and K-valleys are highlighted by arrows, appearing as symmetric replicas on the left and right of the main band. Despite the broad manifold of bulk states and significant out-of-plane dispersion at the -point, the satellite features remain clearly discernible. This is benefited by the high degree of interfacial cleanliness and uniformity in the sample. The dispersion at the K-valley, along with the corresponding momentum-distribution curves (MDCs) and fits, are displayed in Figure 12, insets b and c.

[0055] Figure 13 illustrates more details of the ARPES fitting 1300, according to an example embodiment. As revealed by the fit peak positions, the two satellite bands are symmetric about the main band, supporting their origin as backfolded replicas rather than originating from two adjacent domains which typically produce a superposition of two sets of bands with a random momentum offset. Both main and replica bands exhibit nearly energyindependent linewidths of comparable magnitudes. This subtle difference can be taken as a measure of convoluted rotational disorder of the crystal, placing an upper limit on the angular variation up to ~0.04e across the beam spot of (30x5) pm2, in agreement with the PFM and LEED measurements.

[0056] There is evidence to suggest that these satellite bands arise due to the atomic reconstruction of the constituent layers rather than the interlayer interaction. The periodic structural modulations from PLD give rise to distinct signature of satellite replicas in the reciprocal space, observable in both electron diffraction and photoemission spectroscopy. The surface sensitivity of ARPES imposes stringent requirements on the design and quality of vdW twist interface. In this regard, the presently disclosed pristine twist vdW interface enables the formation of well-defined PLD structures of notably higher consistent quality than those typically found in microscopic twist-and-stack samples. The enhanced structural quality is reflected in both the clear moire contrast observed in PFM and the clear resolution of K-point band features in ARPES measurements. In this system, the strong out-of-plane dispersion of the bulk M0S2 makes it challenging to energetically isolate the moire minibands, a prerequisitefor accessing correlation-driven phenomena. Nonetheless, the observed periodic reconstruction and electronic signatures suggest that the presently disclosed heterostructures could serve as a promising platform for exploring triangular lattice models within the framework of a “quantum simulator.”

[0057] To further elucidate the origin of the replicas, the constant energy contour (CEC) is examined at the energy E-Ev = -0.62 eV. Figure 14 illustrates a simulation of ARPES on twisted M0S2 moire structure and constant energy contour (CEC) diagrams 1400, according to an example embodiment. Approximately threefold symmetric faint replica bands around the -and K-valleys are observed. The most prominent features of the CEC can be reproduced through spectral function simulations. As depicted in Figure 12 inset f and Figure 14, the intensity distribution can be fully recreated by considering two sets of mini-bands displaced by the moire reciprocal lattice vector for a twist angle 0 = 4.5 degrees. Both sets exhibit C3 symmetry due to mirror-symmetry breaking induced by the in-plane distortions of the top monolayer. One set follows the orientation of the moire reciprocal vectors, while the other is rotated by 180 degrees. This can be explained by considering the electrons from the first and second topmost bulk layers, respectively, due to the 180-degree rotation between adjacent layers in a 2H crystal structure.

[0058] In general, the replica bands could arise from a combination of two effects: final-state Umklapp scattering of the photoelectrons upon exiting the surface, which is independent of 9, and modification of initial Bloch states by the superlattice potential, which is more pronounced at small twist angles. The final-state effect is a property of the photoemission process itself; whereas the initial-state effect will lend critical insight into how the moire potential directly shapes the electronic structure and tune the properties of the system. Herein, matrix element analysis is performed to evaluate their contributions qualitatively, using a layer and orbital interference model developed for bilayer M0S2. The initial-state effect is highly sensitive to the kinetic energy of the photoelectrons and orbital character of the emitter atoms. The intensity modulation across the trigonally warped main band contour results from intra- and interlayer interference effects, affecting the local orbital make-up of the states around the K-valley. In the Umklapp scattering scenario, the satellite bands should exhibit the same intensity distribution (including its relative orientation) as the original band. However, as shown in the Figure 12, insets f-g and Figure 14, the data contradicts this pattern. Instead, it is found that the outer replica features are best described by rotating the matrix element for the two sets of backfolded bands by 90 and 60 degrees, respectively. This observation underscores the significant influence of the superlattice potential, aligning with the small twist angle 0=4.5ewhich is within the range where correlated phenomena in TMDCs have been previously observed.

[0059] The evolution of the band with varying photon energies hv was also evaluated in example embodiments. Figure 12 inset h demonstrates experimental photon energydependence of the T-K cut at E-Ev= 0.62 eV. Furthermore, Figure 15 illustrates examples of full spectra at selected photon energies 1500, according to an example embodiment. Comparing the experimental data to the simulation in Figure 12 inset i, the simulation qualitatively reproduces the intensity modulation of the main bands, capturing the intensity increase in the energy range 50-70 eV and suppression of the right branch at higher hv. This simulation also assumes that the minibands follow the same Av-dependence as the main bands, i.e. represents a final-state Umklapp scattering scenario. In comparison, the experimental moire minibands exhibit enhancement of the rightmost replica around 60-75 eV, while the inner replicas retain approximately constant intensity across the entire investigated photon energy range. This result suggests that the observed distribution may emerge from a more complex moire-induced effect than a simple final-state diffraction model.

[0060] Figure 16 illustrates experimental LEED patterns and corresponding reciprocal space simulation and schematic of the reconstructed superlattice, 1600. Figure 16, inset a shows an experimental LEED pattern of M0S2 monolayer on bulk moire structure. Figure 16, inset b shows simulated reciprocal space image of a moire superlattice formed by a bulk crystal and a monolayer with periodic lattice distortion (PLD). Figure 16, inset c illustrates a schematic of the reconstructed moire superlattice, showing the underlying bulk structure, the PLD in the monolayer, and their resulting interference pattern.

[0061] Figure 17 illustrates LEED diffraction intensities of the monolayer and moire spots of 7e M0S2 / M0S2 as a function of electron energy 1700, according to example embodiments. Figure 17, inset a, depicts the absolute intensity, whereas Figure 17, inset b, plots the relative intensity ratio.

[0062] Figure 18 illustrates photoluminescence spectra of gold exfoliated monolayers of M0S2, MoSe2, WS2, and WSe2. These photoluminescence measurements of the example embodiment were performed at 10K.

[0063] In summary, the present disclosure presents a rapid and deterministic technique for engineering moire superlattices of twisted vdW systems with exceptional versatility, reproducibility, and precision across macroscopic areas, a level of control not achievable with conventional tear and stack techniques. The approach is broadly applicable across a variety of vdW materials and different mixed dimensionalities, making it highly adaptable for a broadrange of twistronic device applications. The macroscopic size and high quality clean vdW interface of moire structures not only enhances the thermal stability, but also facilitates direct spectroscopic access to key electronic features which has eluded detections due to sample size limitation. Notably, the back folded replicas of moire mini BZ at both T and K point in twisted M0S2 moire structures were directly observed using high resolution ARPES. The structural uniformity and scalability of these systems open promising avenues for applying a broader variety of macroscopic scattering and spectroscopic techniques, paving the way for exploring previously inaccessible quantum phenomena in 2D moire materials.Example Methods

[0064] Figure 19 illustrates a method 1900 of forming the moire twisted bilayers according to example embodiments. The method 1900 may include blocks or steps that may be carried out or performed in any order. Furthermore, steps or blocks may be added or removed within the scope of the present disclosure. The steps or blocks of method 1900 may be carried out once, continuously, periodically, or over discrete amounts of time. Method 1900 may include operations carried out entirely, or in part, by a human. Additionally or alternatively, some or all of the steps or blocks of method 1900 could be carried out by, for example, a robotic system or another type of semiconductor processing system.

[0065] Block 1902 includes providing a first substrate. The substrate includes a plurality of two-dimensional monolayers. The plurality of two-dimensional monolayers includes an exposed monolayer. In some embodiments, the substrate may include a van der Waals bulk crystal material. In some examples, the substrate could include a freshly cleaved bulk crystal. In such scenarios, the cleaved bulk crystal may include at least one of: graphite, M0S2, WS2, MoSe2, WSe2, MoTe2, ReS2, or hBN. It will be understood that other precursor materials, such as WTe2, and, ReSe2 are possible and contemplated. Method 1900 could be performed on a wide variety of two-dimensional materials. Additionally or alternatively, it will be understood that precursor materials having various electrical properties (e.g., insulating, semiconducting, conducting metals, etc.) are possible and contemplated.

[0066] Block 1904 includes pressing a first metal surface onto the first substrate by way of the exposed monolayer. In some embodiments, pressing the first metal surface onto the first substrate may cause an interaction between vdW and typical chemical bonds.

[0067] In example embodiments, the first metal surface is coupled to a handling structure. In such scenarios, the handling structure may include a polyvinylpyrrolidone (PVP) layer coupled to the metal surface and a thermal release tape layer coupled to the PVP layer.Alternatively, the handling structure may include a polycarbonate (PC) layer coupled to the metal surface and a polydimethylsiloxane (PDMS) layer coupled to the PC layer. In embodiments where a bilayer is being formed and there are multiple metal surfaces and multiple handling structures, the handling structures for each of the different layers may be made with same or different materials. It will be understood that other types of handling structures are possible and contemplated.

[0068] Block 1906 includes removing the metal surface from the substrate and thereby exfoliating the exposed monolayer from a remaining monolayer stack. In various embodiments, removing the metal surface from the substrate overcomes a van der Waals adhesion force between the exposed monolayer and the remaining monolayer stack.

[0069] Block 1908 includes providing a second substrate. The second substrate may be the same material or a different material than the first substrate material. Any of the possible candidate materials described for the first substrate material may be used for the second substrate material including graphite, M0S2, WS2, MoSe2, WSe2, MoTe2, ReS2, or hBN. It will be understood that other substrate materials are possible and contemplated.

[0070] Block 1910 includes pressing a second metal surface onto the second substrate by way of the exposed monolayer. The material of the second metal surface may be the same or different from the material of the first metal surface.

[0071] Block 1912 includes removing the second metal surface from the second substrate and thereby exfoliating the exposed monolayer from a remaining monolayer stack. In various embodiments, removing the second metal surface from the second substrate overcomes a van der Waals adhesion force between the exposed monolayer and the remaining monolayer stack.

[0072] Block 1914 includes rotating the first exposed monolayer with respect to the second exposed monolayer. In some examples, rotating the first exposed monolayer includes controllably rotating the exposed monolayer by a predetermined angle. The selection of the value of the predetermined angle may allow for the tuning of specific material properties such as superconductivity and anomalous Hall Effect. In some embodiments, the predetermined angle may be a “magic angle” for desired properties for the given material system. Any angle in the range of 0°-360° is possible. The magic angle refers to specific small twist angle (typically on the order of 3°-5° in transition metal dichalcogenides bilayers, and approximately 1° in graphene bilayers) at which flat electronic bands form, enabling the emergence of strongly correlated quantum phases.

[0073] While a few specific “magic angles” are often emphasized — such as the well-known 1.08° in twisted bilayer graphene — there are, in fact, a multitude of magic angles across various twisted systems that could be realized using this method. As the twist angle increases or decreases, additional magic angles can emerge, including at smaller angles like -0.5°. Moreover, when additional layers are introduced (e.g., in twisted trilayer systems), the relevant angles shift — for instance, chiral trilayer graphene exhibits a magic angle around 1.6°, but this too depends on the stacking method. Additionally, even angles not traditionally labeled “magic” can host strongly correlated or otherwise significant physical phenomena.

[0074] Block 1916 includes coupling the first exposed monolayer to the second exposed monolayer in a face-to-face assembly so as to form a bilayer. In some embodiments, the bilayer forms a macroscopic moire structure. In such scenarios, the macroscopic moire structure could have an area of more than 1 cm2and does not exhibit bubbles. Additionally or alternatively, the macroscopic moire structure could exhibits consistent and uniform surface characteristics across distances of more than one millimeter as measured by piezoresponse force microcopy (PFM) or torsional force microscopy (TFM).

[0075] In various examples, the method 1900 may also include removing the handling structure from the first metal surface, removing the first metal surface from the first exposed monolayer, transferring the first exposed monolayer, the second exposed monolayer, and the second metal surface to a target substrate, removing the handling structure from the second metal surface, and removing the second metal surface from the second exposed monolayer.

[0076] In some example embodiments, removing the handling structure from the metal surface could include at least one of: a thermal treatment, a solvent rinse, or an etch process.

[0077] In various examples, the first metal surface and second metal surfaces could include Au. In such scenarios, removing the metal surface from the exposed monolayer includes a KI / b etch process.

[0078] In some examples, the target substrate may be Si with a SiCh layer.

[0079] In some embodiments, at least some steps of method 1900 may be performed in a laminar flow bench. Additionally or alternatively, at least some steps of the method 1900 may be performed in a vacuum environment. Yet further, at least some steps of the method could be performed using roll-to-roll fabrication processes.

[0080] Figure 20 illustrates a method 2000, of forming twisted moire monolayer on bulk structures, according to example embodiments. Method 2000 may include one or more steps or blocks, which may be carried out in any order. Furthermore, steps or blocks may be added or removed within the scope of the present disclosure. The steps or blocks of method2000 may be carried out once, continuously, periodically, or over discrete amounts of time. Method 2000 may include operations carried out entirely, or in part, by a human. Additionally or alternatively, some or all of the steps or blocks of method 2000 could be carried out by, for example, a robotic system or another type of semiconductor processing system.

[0081] Block 2002 includes providing a substrate. The substrate includes a plurality of two-dimensional monolayers. The plurality of two-dimensional monolayers includes an exposed monolayer. In some embodiments, the substrate may include a van der Waals bulk crystal material. In some examples, the substrate could include a freshly cleaved bulk crystal. In such scenarios, the cleaved bulk crystal may include at least one of: graphite, M0S2, WS2, MoSe2, ReS2, WSe2, MoTe2, or hBN. It will be understood that other precursor materials, such as WTe2, ReSe2 are possible and contemplated. Method 2000 could be performed on a wide variety of two-dimensional materials. Additionally or alternatively, it will be understood that precursor materials having various electrical properties (e.g., insulating, semiconducting, conducting metals, etc.) are possible and contemplated.

[0082] Block 2004 includes pressing a metal surface onto the substrate by way of the exposed monolayer. In various examples, pressing the metal surface onto the substrate could form two-dimensional van der Waals bonds between the metal surface and the exposed monolayer.

[0083] In example embodiments, the metal surface is coupled to a handling structure. In such scenarios, the handling structure includes a polyvinylpyrrolidone (PVP) layer coupled to the metal surface and a thermal release tape layer coupled to the PVP layer. It will be understood that other types of handling structures are possible and contemplated.

[0084] Block 2006 includes removing the metal surface from the substrate and thereby exfoliating the exposed monolayer from a remaining monolayer stack. In various embodiments, removing the metal surface from the substrate overcomes a van der Waals adhesion force between the exposed monolayer and the remaining monolayer stack.

[0085] Block 2008 includes rotating the exposed monolayer with respect to a reference monolayer stack. The reference monolayer stack is the remaining monolayer stack after exfoliation or a different monolayer stack. In some examples, rotating the exposed monolayer includes controllably rotating the exposed monolayer by a predetermined angle.

[0086] Block 2010 includes pressing the exposed monolayer onto the reference monolayer stack. In some embodiments, pressing the exposed monolayer onto the reference monolayer stack forms a macroscopic moire structure. In such scenarios, the macroscopic moire structure could have an area of more than 1 cm2and does not exhibit bubbles.Additionally or alternatively, the macroscopic moire structure could exhibits consistent and uniform surface characteristics across distances of more than one millimeter as measured by piezoresponse force microcopy (PFM) or torsional force microscopy (TFM).

[0087] In various examples, the method 2000 may also include removing the handling structure from the metal surface and removing the metal surface from the exposed monolayer. In such scenarios, removing the handling structure from the metal surface could include at least one of: a thermal treatment, a solvent rinse, or an etch process.

[0088] In some examples, the metal surface could include Au. In such scenarios, removing the metal surface from the exposed monolayer comprises a Kl / h etch process. In some embodiments, at least some steps of method 2000 may be performed in a laminar flow bench. Additionally or alternatively, at least some steps of the method 2000 may be performed in a vacuum environment. Yet further, at least some steps of the method could be performed using roll-to-roll fabrication processes.

[0089] While embodiments have been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art, from a study of the drawings, the disclosure and the appended claims. In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used. Any reference signs in the claims should not be construed as limiting the scope.

Claims

CLAIMSWhat is claimed is:

1. A method of manufacturing comprising:providing a first substrate, the first substrate comprising a plurality of two-dimensional monolayers, wherein the plurality of two-dimensional monolayers comprises a first exposed monolayer;pressing a first metal surface onto the first substrate by way of the first exposed monolayer;removing the first metal surface from the first substrate and thereby exfoliating the first exposed monolayer;providing a second substrate, the second substrate comprising a plurality of two-dimensional monolayers, wherein the plurality of two-dimensional monolayers comprises a second exposed monolayer;pressing a second metal surface onto the second substrate by way of the second exposed monolayer;removing the second metal surface from the second substrate and thereby exfoliating the second exposed monolayer;rotating the first exposed monolayer with respect to the second exposed monolayer; andcoupling the first exposed monolayer to the second exposed monolayer, in a face-to-face assembly so as to form a bilayer.

2. The method of claim 1, wherein the first substrate and the second substrate comprise a van der Waals bulk crystal material.

3. The method of claim 1,wherein pressing the first metal surface onto the first substrate forms two-dimensional van der Waals bonds between the first metal surface and the first exposed monolayer; and wherein pressing the second metal surface onto the second substrate forms two-dimensional van der Waals bonds between the second metal surface and the second exposed monolayer.

4. The method of claim 1,wherein removing the first metal surface from the first substrate overcomes a van der Waals adhesion force between the first exposed monolayer and a first remaining monolayer stack; andwherein removing the second metal surface from the second substrate overcomes a van der Waals adhesion force between the second exposed monolayer and a second remaining monolayer stack.

5. The method of claim 1, wherein rotating the first exposed monolayer comprises controllably rotating the first exposed monolayer by a predetermined angle.

6. The method of claim 5, wherein the predetermined angle comprises a specific small twist angle at which flat electronic bands form in the bilayer, causing strongly correlated quantum phases.

7. The method of claim 5, wherein selecting a value of the predetermined angle allows for tuning of specific electronic material properties such as superconductivity and anomalous Hall Effect.

8. The method of claim 1, wherein the first metal surface and second metal surface are each coupled to a handling structure, wherein the handling structure comprises at least one of:a first handling structure comprising a polyvinylpyrrolidone (PVP) layer coupled to the metal surface and a thermal release tape layer coupled to the PVP layer; ora second handling structure comprising a polycarbonate (PC) layer coupled to the metal surface and a polydimethylsiloxane (PDMS) layer coupled to the PC layer.

9. The method of claim 8, wherein the method further comprises:removing the handling structure from the first metal surface; andremoving the first metal surface from the first exposed monolayer,transferring the first exposed monolayer, the second exposed monolayer, and the second metal surface to a target substrate;removing the handling structure from the second metal surface; andremoving the second metal surface from the second exposed monolayer.

10. The method of claim 9, wherein removing the handling structure from the first metal surface or the second metal surface comprises at least one of: a thermal treatment, a solvent rinse, or an etch process.

11. The method of claim 1, wherein the first metal surface and the second metal surface comprise Au.

12. The method of claim 9, wherein removing the first metal surface and the second metal surface from the first exposed monolayer and the second exposed monolayer comprises a KI / I2 etch process.

13. The method of claim 9, wherein the target substrate comprises a SiCh layer on a Si substrate.

14. The method of claim 1, wherein the bilayer comprises a macroscopic moire bilayer.

15. The method of claim 14, wherein the macroscopic moire bilayer has an area of more than 1 cm2and does not exhibit bubbles.

16. The method of claim 14, wherein the macroscopic moire bilayer exhibits consistent and uniform surface characteristics across distances of more than one millimeter as measured by piezoresponse force microcopy (PFM) or torsional force microscopy (TFM).

17. The method of claim 1, wherein providing the first substrate or second substrate comprises providing a freshly cleaved bulk crystal, wherein the cleaved bulk crystal comprises at least one of: graphite, M0S2, WS2, MoSe2, WSe2, MoTe2, WeTe2, ReS2, or hBN.

18. A method of manufacturing comprising:providing a substrate, the substrate comprising a plurality of two-dimensional monolayers, wherein the plurality of two-dimensional monolayers comprises an exposed monolayer;pressing a metal surface onto the substrate by way of the exposed monolayer;removing the metal surface from the substrate and thereby exfoliating the exposed monolayer from a reference monolayer stack, wherein the reference monolayer stack comprises a remaining monolayer stack following exfoliation or another monolayer stack; rotating the exposed monolayer with respect to the reference monolayer stack; and pressing the exposed monolayer onto the reference monolayer stack.

19. The method of claim 18, wherein the substrate comprises a van der Waals bulk crystal material.

20. The method of claim 18, wherein the method further comprises:coupling the metal surface to a handling structure, wherein the handling structure comprises:a polyvinylpyrrolidone (PVP) layer coupled to the metal surface; and a thermal release tape layer coupled to the PVP layer;after pressing the exposed monolayer onto the reference monolayer stack, removing the handling structure from the metal surface; andremoving the metal surface from the exposed monolayer.

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