A multi-layer structure, a superconducting apparatus, and a method for manufacturing a superconducting apparatus
Patent Information
- Authority / Receiving Office
- EP · EP
- Patent Type
- Applications
- Current Assignee / Owner
- IQM FINLAND OY
- Filing Date
- 2023-06-30
- Publication Date
- 2026-05-06
Smart Images
Figure FI2023050411_02012025_PF_FP_ABST
Abstract
Description
[0001] A MULTI-LAYER STRUCTURE, A SUPERCONDUCTING APPARATUS, AND A METHOD FOR MANUFACTURING A SUPERCONDUCTING APPARATUS
[0002] TECHNICAL FIELD OF THE INVENTION
[0003] The invention relates to superconducting devices in general. More specifically, the invention relates to a multi-layer structure configured to be coupled to a superconducting device, and to a superconducting apparatus comprising such multi-layer structure. The invention also relates to a method of manufacturing such superconducting apparatus.
[0004] BACKGROUND OF THE INVENTION
[0005] Superconducting devices have many potential uses including e.g. quantum devices, sensor devices, and in connection with cryogenic applications. The performance of many of these superconducting devices is hindered by the presence of quasiparticles in the device.
[0006] Quasiparticles result from the breaking apart of Cooper pairs, which are present in superconductors, when one of the electrons in the pair is excited to a higher energy level.
[0007] At low temperatures, i.e. well below the critical temperature of superconducting materials, only Cooper pairs should be found in the superconducting materials. However, it has been demonstrated that non-equilibrium quasiparticles, i.e. unpaired electrons or quasiparticle excitations (also simply termed quasiparticles herein), are found in superconducting materials at temperatures well below their critical temperature. The reasons for such excitations are currently at least partially unknown, although there have been some indications that environmental radioactive materials and cosmic-ray bursts may generate the quasiparticles. Thus, the generation of quasiparticles may be difficult to avoid in devices in any practical solutions, and it would be advantageous to find solutions for reducing the density or mitigation of quasiparticles in superconducting devices.
[0008] The non-equilibrium quasiparticles negatively affect the functioning of superconducting devices. For example, the quasiparticle reduces the quality factor of superconducting resonators. In the case of superconducting devices being qubits and comprising a Josephson junction, for instance, quasiparticles can tunnel to the Josephson Junction and cause qubit energy decay and decoherence, which limits the lifetime and stability of the qubits. Furthermore, it is known that one side effect of the Single Flux Quantum (SFQ) pulses, used for scaling up the qubits, is the generation of quasiparticles that can then limit the gate fidelities. As further disadvantages related to qubits, it is known that the presence of quasiparticles affect energy levels of qubits, leading to shifts of qubit frequencies and that quasiparticles may limit the relaxation time of superconducting qubits. In superconducting qubits, it has been firmly established both theoretically and experimentally that quasiparticle tunneling causes qubit energy decay and dephasing.
[0009] The mitigation of effects of quasiparticles on qubits may provide more stable and long-lived qubits, which can facilitate the further development of quantum computing devices.
[0010] Another example of superconducting devices where quasiparticles may cause problems are Josephson-junction based sensor devices, where measurements dependent on current flowing through a Josephson junction. Here, tunnelling quasiparticles may cause these devices to not function as desired.
[0011] There have been attempts to reduce the number of quasiparticles in superconducting devices, by using methods or structures known as quasiparticle traps. It is known that vortices may be used for such purposes, but this requires cooling in a magnetic field, which makes the method unsuitable for many devices, such as 2D transmons. Vortices are also difficult to control and a large number of them could negatively influence the performance of a superconducting device.
[0012] Other prior art quasiparticle traps may comprise a normal-conductivity metal layer that is coupled to the superconducting device, such that they are separated by an insulator layer to provide a superconductor - insulator - normal-conductivity metal (SIN) junction. These traps may evacuate quasiparticles from a superconducting material of a superconducting device by quasiparticles tunneling through to the metal material, and upon relaxation of the quasiparticle below the superconducting gap in the normal-conductivity metal layer, the density of quasiparticles present in the superconducting device is thus reduced. This results in a more stable and long-lived superconducting device. Such prior art quasiparticles traps are known from e.g. A. Hosseinkhani, R.-P. Riwar, R. J. Shoelkopf, L. I. Glazman, G. Catelani, Phys. Rev. App. 8, 064028, 2017, A. Hosseinkhani and G. Catelani, Phys. Rev. B 97, 054513 (2018), and R.-P. Riwar, A. Hosseinkhani, L. D. Burkhart, Y. Y. Gao, R. J. Schoelkopf, L. I. Glazman, G. Catelani, Phys. Rev. B 94, 104516 (2016).
[0013] However, it is known that quasiparticle back tunneling is a problem with the abovedescribed SIN structure of normal-conductivity metal traps. In such back tunneling, quasiparticles with energies above the superconducting gap of the superconducting material can escape from the normal-conductivity metal trap and tunnel back into the superconducting material. The rate of this harmful process is significantly enhanced at energies very close and above the superconducting gap of the superconducting material due to the divergent behavior of the density of states in Bardeen-Cooper-Schrieffer (BOS) superconductors, where the DOS becomes infinite. It has been demonstrated for a structure in which the superconducting material is aluminium, and the normal-metal trap is Copper, that the effective quasiparticle trapping rate is about two orders of magnitude smaller than the rate at which quasiparticles tunnel into the normal-conductivity metal layer, due to the back tunneling.
[0014] It would thus be beneficial to discover a more efficient way to reduce the density of quasiparticles in superconducting devices, especially one that could be utilized with e.g. 2D transmons.
[0015] SUMMARY OF THE INVENTION
[0016] An object of the invention is to alleviate at least some of the problems of the prior art. In accordance with one aspect of the present invention a multi-layer structure is provided to reduce the quasiparticle density of a superconducting device, said multi-layer structure comprises at least a first superconducting material layer, at least one trapping material layer, at least one insulating layer, and at least one tunneling layer, wherein the tunneling layer is provided between the trapping material layer and the first superconducting material layer. Said multi-layer structure is configured to be coupled to a superconducting device via the insulating layer such that the insulating layer is provided between the superconducting device and the first superconducting material layer.
[0017] The present invention may provide a multi-layer structure for a superconducting device that more efficiently reduces the density of quasiparticles in a superconducting device than in the prior art.
[0018] The amount of quasiparticles that are present in a superconducting device and / or at the vicinity of a Josephson junction provided in a superconducting device or coupled to such device may be reduced with the present multi-layer structure as compared to trap structures of the prior art that may be provided in connection with superconducting devices.
[0019] The present invention may conceptually be considered as a combination of utilizing a trapping material for quasiparticle trapping and superconducting material band gap engineering in a single structure.
[0020] A thickness of the tunneling layer may be inferior to a thickness of the insulating layer.
[0021] The material of the insulating layer and of the tunneling layer may be the same material or they may be a different material.
[0022] A resistance of the tunneling layer may be configured to be lower than a resistance of the insulating layer, preferably 1-2 orders of magnitude lower. By configuring the resistances suitably, quasiparticles that are removed from the superconducting device into the multilayer structure may exhibit less tunneling back into the superconducting device than that associated with prior art trap structures.
[0023] The at least one trapping material layer may comprise a normal-conductivity metal material and / or a superconducting material, said superconducting material having a lower superconducting bandgap than the superconducting material of the first superconducting material layer.
[0024] The first superconducting material layer may be configured to provide a superconducting energy gap that is smaller than a superconducting energy gap of a superconducting material element of the superconducting device that is configured to be coupled to the multi-layer structure.
[0025] The first superconducting material layer may comprise a material which is the same as a material of the superconducting material of the superconducting device, in particular of the portion of the superconducting device to be coupled to the insulating layer. A thickness of the first superconducting material layer may be different or equivalent to a thickness of the superconducting material element.
[0026] A thickness of the first superconducting material layer and / or a thickness of the trapping material layer may be comprised between 20-500 nm, preferably between 80-200 nm.
[0027] In one embodiment of the invention, a superconducting apparatus may be provided, comprising at least one multi-layer structure as described above and at least one superconducting device comprising at least a superconducting material element, wherein the multi-layer structure is coupled to at least one superconducting device, in particular to the superconducting material element of the at least one superconducting device, more in particular to a portion of the superconducting material element of the superconducting device, via the insulating layer.
[0028] An insulating layer of the at least one multi-layer structure of a superconducting apparatus may be sandwiched between the at least first superconducting material layer and the superconducting material element.
[0029] In embodiments of a superconducting apparatus, the multi-layer structure may be configured to provide a tunneling rate of quasiparticles from the at least first superconducting material layer to the trapping material layer that is superior to a tunneling rate of quasiparticles from the superconducting device to the at least first superconducting material layer of the multi-layer structure. In particular, from the superconducting element of the superconducting device to the at least first superconducting material layer of the multilayer structure.
[0030] In embodiments of a superconducting apparatus, the multi-layer structure may be configured to reduce a tunneling rate of quasiparticles from the trapping material layer to the superconducting device, in particular from the trapping material layer to the superconducting element of the superconducting device.
[0031] In embodiments of a superconducting apparatus, the multi-layer structure may be configured to provide a net trapping rate of quasiparticle that is higher than the net trapping rate of quasiparticles of a trapping material layer coupled to a superconducting device, such that the tunneling of quasiparticles from the trapping material layer to the at least first superconducting material layer is reduced.
[0032] In embodiments of a superconducting apparatus, at least one superconducting device may comprise at least one Josephson junction or be connectable with at least one Josephson junction.
[0033] In embodiments of a superconducting apparatus, at least one multi-layer structure may be positioned adjacent to a Josephson junction along a longitudinal axis of the superconducting device, preferably such that such that a distance from the multi-layer structure to a Josephson junction is 5 to 10 times the coherence length of the superconducting material of the superconducting element of the superconducting device. As an example, when using aluminium as superconducting material, the distance from the multi-layer structure to a Josephson junction may be within the range of 10 to 50 pm, preferably 20 to 40 m.
[0034] At least one superconducting device may be at least part of a qubit device.
[0035] A superconducting device may be or may comprise at least one superconducting logic device, with logic based on rapid single flux quantum logic, reciprocal quantum logic, or adiabatic quantum flux parametron logic. A superconducting apparatus may comprise a plurality of multi-layer structures provided next to each other laterally on at least one of the at least one superconducting device, in particular multi-layer structures as described above.
[0036] A “superconducting apparatus" refers to a structure comprising a superconducting device and at least one multilayer structure.
[0037] The term “superconducting apparatus” has been applied in this text for the purpose of distinguishing from a “superconducting device” that does not comprise a multi-layer structure according to the invention. A superconducting device may e.g. be a qubit device and a superconducting apparatus may be a qubit device comprising at least one multilayer structure.
[0038] Another object of the invention relates to a method of manufacturing a superconducting apparatus as described above, which may comprise providing at least one superconducting device comprising at least a superconducting material element on a substrate, and providing at least one multi-layer structure as described above, characterized in that the at least one multi-layer structure is provided on a surface of at least one superconducting device.
[0039] A step of providing at least one multi-layer structure may comprise a step of providing an insulating layer on a surface of at least a portion of the superconductor material element of the at least one superconducting device.
[0040] A step of providing at least one multi-layer structure may comprise providing more than one multi-layer structure, wherein the multi-layer structures are provided side-by-side on at least one of the at least one superconducting device, in particular on the superconducting element of at least one of the at least one superconducting device.
[0041] The novel features which are considered as characteristic of the invention are set forth in particular in the appended claims. The invention itself, however, both as to its construction and its method of operation, together with additional objects and advantages thereof, will be best understood from the following description of specific example embodiments when read in connection with the accompanying drawings.
[0042] BRIEF DESCRIPTION OF THE DRAWINGS
[0043] Next the invention will be described in greater detail with reference to exemplary embodiments in accordance with the accompanying drawings, in which:
[0044] Figure 1A schematically illustrates a multi-layer structure according to an embodiment of the invention.
[0045] Figure 1 B schematically illustrates a superconducting apparatus according to an embodiment of the invention.
[0046] Figure 2 depicts densities of states in a superconducting apparatus according to one exemplary embodiment of the invention, Figure 3A illustrates a top view of a schematic of a superconducting apparatus according to another embodiment of the invention,
[0047] Figure 3B illustrates a side view of a schematic of a superconducting apparatus as shown in Figure 3A,
[0048] Figure 3C illustrates a side view of a schematic of a superconducting apparatus according to another embodiment of the invention,
[0049] Figure 4 illustrates a top view of a schematic of a superconducting apparatus according to another embodiment of the invention,
[0050] Figure 5A shows a top view of a superconducting apparatus according to an embodiment of the invention,
[0051] Figure 5B shows a top view of a superconducting apparatus according to another embodiment of the invention, and
[0052] Figure 6 illustrates a flow chart of a method of manufacturing a superconducting apparatus according to an exemplary embodiment of the invention.
[0053] DETAILED DESCRIPTION
[0054] All figures depicted should be considered as schematic examples and e.g. the proportions of different layers or other components are not shown to scale.
[0055] Figure 1A shows one example of an embodiment of a multi- layer structure 102 according to the invention. The multi-layer structure 102 is configured to be coupled to a superconducting device 106.
[0056] The multi-layer structure 102 comprises at least one first superconducting material layer 108, at least one trapping material layer 118, at least one insulating layer 1 14 and at least one tunneling layer 116.
[0057] The at least one first superconducting material layer 108 has a first surface 110 and a second surface 112. The first superconducting material layer 108 is provided sandwiched between the at least one tunneling layer 116 and the at least one insulating layer 114.
[0058] The insulating layer 114 is arranged in connection with at least a portion of the first surface 110 of the first superconducting material layer 108. In Figure 1A, the insulating layer 114 is provided on the whole first surface 110 of the first superconducting material layer 108.
[0059] The insulating layer 114 is configured to couple the superconducting device 106 via its surface 106a. As shown in Figure 1A, the insulating layer 114 is configured to couple at least a portion of a superconducting device 106, to the multi-layer structure 102, in particular via the first surface 110 of the first superconducting material layer 108 of the multi-layer structure 102. The insulating layer 114 may directly contact at least a portion of the superconducting device 106. In Figure 1A, the insulating layer 114 is configured to be provided in contact with the whole surface of the superconducting device 106. The insulating layer 114 comprises an insulating material such as an oxide material. The insulating layer 114 can also comprise a combination of insulating layers made of different oxide materials.
[0060] The multi-layer structure 102 can be coupled to the superconducting device 106 via a superconducting material element 104 of a superconducting device. In a variant of the embodiment, the multi-layer structure 102 can be coupled to the superconducting device 106 via another layer of the superconducting device 106, not necessarily the superconducting material element 104 of the superconducting device 106.
[0061] A tunneling layer 116 is arranged on at least a portion of the second surface 112 of the first superconducting material layer 108. In Figure 1A, the tunneling layer 116 is provided on the whole second surface 112 of the first superconducting material layer 108.
[0062] At least one trapping material layer 118 is further arranged on at least a portion of the tunneling layer 116. The tunneling layer 116 may be considered to have a first surface 116a and second surface 116b, wherein the first surface 116a is arranged to contact the first superconducting material layer 108 and the second surface 116b is arranged to contact the trapping material layer 118. The tunneling layer 116 is provided in sandwich between the trapping layer 118 and the first superconducting material layer 108.
[0063] A resistance of the tunneling layer 116 may be configured to be lower than a resistance of the insulating layer 114. The tunneling layer 116 can be made of any material which has a lower resistance than the insulating layer 114. In some embodiments, the tunneling layer 116 may also be an insulating layer. For example, the tunneling layer 116 could be a native oxide or an oxide layer being deposited on the first superconducting material layer 108, or a combination of oxide layers. In that case, the tunneling layer 116 may be considered as a second insulating layer 116 and the insulating layer 114 may be considered as a first insulating layer 114. The tunneling layer 116 can also be made of the same material as the insulating layer 114 if the thicknesses of said layers are selected appropriately.
[0064] A thickness t of the tunneling layer 116 may be comparable to oxide layers typically used in junctions. The thickness of the tunneling layer 116 may be e.g. 0.1-5 nm, 0.5-2 nm, or about 1 nm.
[0065] The thickness of the insulating layer 114 is larger than the thickness of the tunneling layer 116 to provide an increased resistance and to ensure that the resistance at the interface of the tunneling 116 is 1-2 orders of magnitude smaller. The thickness of the insulating layer 114 may be 0.1-15 nm, such as 1-10 nm. But, in a variant, the thickness of the insulating layer 114 may also be about the same as the thickness of the tunneling layer 116.
[0066] Suitable resistances may here be exhibited inherently through material selections of the multi-layer structure 102, as a resistance of a SIS junction may in general be larger that of a resistance of an SI N junction. With the selected resistances, coupling or coupling strength between the first superconducting material layer 108 and the superconducting material element 104 may therefore be weaker than the coupling strength between the first superconducting material layer 108 and the trapping material layer 118 of the multi-layer structure 102.
[0067] The resistance between the first superconducting material layer 108 and the superconducting material element 104 and / or between the first superconducting material layer 108 and the trapping material layer 118 may be further tuned by selecting suitable thicknesses of the insulating layer 114, and / or the tunneling layer 116.
[0068] Preferably, a resistance between the first superconducting material layer 108 and the trapping material layer 118 may be configured to be at least 1-2 orders of magnitude lower than a resistance between the first superconducting material layer 108 and the superconducting material element 104.
[0069] In terms of numerical values, in some embodiments a resistance between the first superconducting material layer 108 and the trapping material layer 118 may be under 500 Q / pm2, preferably 5-500 Q / pm2, more preferably 100-430 Q / pm2. These values of resistance correspond to the values of resistance of the tunneling layer 116.
[0070] The superconducting material element 108 may comprise aluminium, tantalum, or niobium nitride to name a few examples, or an alloy of these materials. The first superconducting material layer 108 may comprise a material that is the same as the material of the superconducting material element 104 or it may comprise a different superconducting material.
[0071] The trapping material layer 118 may comprise a normal-conductivity material, for instance copper or silver, or any alloy of these materials. The trapping material layer 118 may additionally or alternatively comprise a superconducting material which has a superconducting bandgap lower than the superconducting bandgap of the adjacent first superconducting material layer 108.
[0072] Figure 1 B illustrates a multi-layer structure 102 as shown in Figure 1A coupled to superconducting device 106.
[0073] The superconducting device 106 may comprise at least a superconducting material element 104 and a substrate 002. The at least one superconducting material element 104 may be provided on the substrate 002. The substrate 002 can be made of silicon, any silicon-based material or sapphire-based substrate.
[0074] The multi-layer structure 102 is coupled to the superconducting device 106 via the at least one superconducting material element 104. The at least one superconducting material element 104 may be also called a second superconducting material layer 104. The superconducting material element 104 may comprise aluminium, tantalum, or niobium nitride to name a few examples, or an alloy of these materials. In this embodiment, the structure obtained and shown in Figure 1 B corresponds to a Superconductor-lnsulator-Superconductor-lnsulator-Normal (Metal), also denominated as SISIN structure or to a Superconductor-lnsulator-Superconductor-lnsulator- Superconductor, also denominated as SISIS structure. In comparison, the structures mentioned in the state of the art for quasiparticle trapping usually relate to SIN structures, namely Superconductor-lnsulator-Normal (Metal), or SN structures, namely Superconductor-Normal (Metal). The superconducting device 106 may be e.g. a sensor device, a cryogenic device, or a quantum device.
[0075] The superconducting device 106 may also comprise or be connectable with at least one Josephson junction. For example, the superconducting device may comprise at least one qubit.
[0076] The multi-layer structure 102 and the superconducting device 106 can be considered as separate entities or they can be considered to form a superconducting apparatus 300, wherein they are connected to each other, as shown in Figure 1 B.
[0077] The multi-layer structure 102 is configured to vacate quasiparticles from the superconducting device 106. The multi-layer structure 102 may be configured to vacate quasiparticles from at least the superconducting material element 104 of the superconducting device 106. The term “vacate quasiparticles” may refer to the multi-layer structure providing a structure for quasiparticles originally present in the superconducting device to transfer or tunnel into. Thus, the number or density of quasiparticles present in the superconducting device 106 may then be reduced compared to the superconducting device 106 not being coupled to the multi-layer structure 102.
[0078] The vacating / removing of quasiparticles from the superconducting device 106 may improve the functioning of the superconducting device 106 since the presence of quasiparticles in superconducting devices hinder their functioning I performance.
[0079] The multi-layer structure 102 may be especially advantageous in superconducting devices 106 comprising at least one Josephson junction, where the at least one superconducting material element 104 of the superconducting device 106 is in tunnel contact via a barrier / insulating layer to at least one other superconducting material element, as will be demonstrated further herein. The multi-layer structure 102 may prevent at least some of the quasiparticles originally present in the superconducting material element 104 of the superconducting device 106 from reaching the Josephson junction, and thus from tunneling through to the Josephson junction, which would result in a dysfunction of the device. The term “Josephson junction” here is used to refer to a further superconductor-insulator- superconductor junction or also called SIS junction that is provided in a superconducting device 106. In this case, the further SIS junction is different and separate from the SIS junction made from the superconducting material element 104, the insulating layer 114 and the superconducting material layer 118 provided between the superconducting material element 104 and part of the multi-layer structure 102.
[0080] A superconducting device 106 may comprise a plurality of superconducting material elements 104, which may be identical or they may differ from each other. A first superconducting material element 104 of a superconducting device 106 may be coupled to one or more multi-layer structures 102 and a second or subsequent superconducting material element 104 may be coupled to no multi-layer structures 102 or one or more multilayer structures, as will be demonstrated further below.
[0081] The multi-layer structure 102 may be configured to allow quasiparticles to tunnel into the multi-layer structure 102 from the superconducting device 106 and trap some of the quasiparticles into the trapping layer 118 of the multi-layer structure 102 and thus reduce a number of quasiparticles present in the superconducting device 106.
[0082] The multi-layer structure may be configured to reduce or prevent to at least some selected degree, the returning or backscattering of tunneled quasiparticles from the multi-layer structure 102 back into the superconducting device 106. The tunneling back of quasiparticles may be reduced at least in comparison to prior art quasiparticle traps I quasiparticle vacating structures that involve for instance only a normal-conductivity metal material layer as a tunneling layer and trapping layer that is directly coupled or via only an insulating layer to the superconducting device 106, the so-called SIN or SN structure. This may be carried out by the multi-layer structure 102 enabling tunneling of quasiparticles firstly from the superconducting material element 104 to the first superconducting material layer 108 through the insulating layer 114 and by the multi-layer structure 102 further enabling the tunneling of these tunneled quasiparticles from the first superconducting material layer 108 into the trapping material layer 118 through the tunneling layer 116.
[0083] The multi-layer structure 102 when coupled to the superconducting device 106 may provide a back tunneling rate of quasiparticles from the first superconducting material layer 108 to the superconducting material element 104 that is below a threshold rate, preferably below a net trapping rate of the multi-layer structure 102.
[0084] The net trapping rate refers to the difference between the tunneling rate of quasiparticles from the superconducting material element 104 to the multi-layer structure 102 or trapping structure 102 and the tunneling rate of quasiparticles from the multi-layer structure 102 to the superconducting material element 104 of the superconducting device 106.
[0085] The multi-layer structure 102 may provide a tunneling rate of quasiparticles from the first superconducting material layer 108 to the trapping material layer 118 that is faster than a tunneling rate of quasiparticles from the superconducting device 106, or at least the superconducting material element 104, to the first superconducting material layer 108 of the multi-layer structure 102.
[0086] The multi-layer structure 102 may be configured to provide a relaxation rate of quasiparticles in the first superconducting material layer 108 that is slower than a tunneling rate of quasiparticles from the superconducting device 106, or at least the superconducting material element 104, to the first superconducting material layer 108 and / or slower than tunneling rate of quasiparticles from the first superconducting material layer 108 to the trapping material layer 118. “Tunneling rate” may refer to a rate of quasiparticles moving or tunneling from one material layer / portion to another. “Relaxation rate” may refer to a rate of quasiparticles losing energy through electron-electron and / or electron-phonon interactions in the same layer, where the quasiparticles remain in the trapping layer, and thus results in a decrease in the number of quasiparticles present in the superconducting layers. A tunneling rate may describe a rate of quasiparticles tunneling in a direction from the superconducting material element 104 towards the first superconducting material layer 108 or a rate of quasiparticles tunneling in a direction from the first superconducting material layer 108 to the trapping material layer 118. A back tunneling rate may describe a rate of quasiparticles returning or tunneling in the opposite direction as the tunneling rate described above, meaning in a direction from the trapping material layer 118 to the first superconducting material layer 108 or in a direction from the first superconducting material layer 108 to the superconducting material element 104.
[0087] By suitable configuration of the multi-layer structural 02, the associated tunneling rates and relaxing rates relating to quasiparticles may be selected or tuned or optimized such that an amount of quasiparticle in the superconducting material element 104 of the superconducting device 106 may be reduced. The amount of quasiparticles may be reduced more efficiently with the multi-layer trapping structure according to the invention than with the prior art trapping structures.
[0088] The multi-layer structure 102 may provide selected resistance or conductance at the interface between the first superconducting material layer 108 and the superconducting material element 104 and / or between the first superconducting material layer 108 and the trapping material layer 118. Resistance (or conductance) may be understood to be inversely proportional to the tunneling rate of quasiparticles at the interface in question. The resistance or conductance may be considered as characterizing a coupling strength at the interface.
[0089] The use of a multi-layer structure 102 according to the invention, denominated as SISIN structure or SISIS structure, in connection with a superconducting device 106, enables to reduce further the density of quasiparticles present in a superconducting device connected to a standard trapping layer, as in the SIN structures.
[0090] Figure 2 shows a graph of the densities of states of a trapping material layer 118, a first superconducting material layer 108, and a superconducting material element 104 in a superconducting device 106 according to an exemplary embodiment of the invention.
[0091] The DOS functions are for illustrative purposes only to show general behavior of the DOS that is exhibited in advantageous embodiments, especially relating to the relative values of DOS between the different material layers / portions. Fig. 2A shows a DOS of the trapping material layer 118 as a function of energy in a superconducting apparatus according to the invention. Fig. 2B shows a DOS of the first superconducting material layer 108 as a function of energy in a superconducting apparatus according to the invention. Fig. 2C shows a DOS of the superconducting material element 104 as a function of energy in a superconducting apparatus according to the invention. The multi-layer structure 102 may be configured to provide a structure where the density of states (DOS) of the first superconducting material layer 108 exhibits a selected profile in relation to the DOS of the superconducting material element 104 of the superconducting device 106. The multi-layer structure 102 may be configured so that the DOS of the first superconducting material layer 108 may be lower than the DOS of the superconducting material element 104 at or near energies corresponding to a superconducting energy gap or bandgap A2 of the superconducting material element 104.
[0092] The multi-layer structure 102 may comprise a first superconducting material layer 108 that exhibits a superconducting energy gap A1 which is lower than the superconducting energy gap A2 of the superconducting material element 104.
[0093] The multi-layer structure 102 may comprise a first superconducting material layer 108 exhibiting a broadened DOS. This broadening of the DOS may lead to the first superconducting material layer 108 comprising significantly lower DOS compared with a BCS superconductor at or near energies corresponding to the superconducting energy gap A2 of the superconducting material element 104.
[0094] The divergent behavior of the BCS superconductor density of states is seen in Fig. 2C, where at and around the superconducting energy gap A2 Of the superconducting material element 104, the DOS varies exponentially. In the prior art where quasiparticle traps are used in a SIN structure, namely superconducting material- insulator- normal-conductivity metal structure , quasiparticles which have tunneled from the superconducting material into the normal metal layer, which acts as the trapping layer, at or near energies close to A2 may effectively escape or tunnel back into the superconducting material as they may not have time to relax in the trapping layer before tunneling back.
[0095] In the SISIN structure or SISIS structure according to the invention, this is not the case. Quasiparticles present in the superconducting material element 104 with energies above the superconducting energy bandgap A2 may tunnel into the first superconducting material layer 108 with a tunneling rate r . Here, they may tunnel further into the trapping material layer 118 with a tunneling rate Advantageously, r is slower (has lower value) than T , and quasiparticles may effectively transfer from the superconducting material element 104 into the trapping material layer 118 due to a lower resistance between the trapping material layer 118 and the first superconducting material layer 108 than between the first superconducting material layer 108 and the superconducting material element 104. Such lower resistances may not be used between the first superconducting material layer 108 and the superconducting material element 104, as it may be harmful for the superconducting device 106. With the lower resistance and a stronger coupling between the superconducting material element 104 and the trapping material layer 118 compared to the coupling between the first superconducting material layer 108 and the superconducting material element 104, it can be expected that » r .
[0096] Some quasiparticles that have reached the trapping material layer 118 may relax at a relaxation rate of within the trapping material layer 118 and are no longer capable of returning I tunneling back to the first superconducting material layer 108. The other quasiparticles may however return to the superconducting material layer 108 with an escape rate of r^fc. Yet, as seen from Fig. 2, due to a broadening of the DOS of the first superconducting material layer 108, this effect (tunneling back of quasiparticles from the trapping material layer 118 to the first superconducting material layer 108) is limited (r^coc n(e)).
[0097] At least a portion of the quasiparticles present in the first superconducting material layer 108 may relax at a relaxation rate of rjeiand may thus not tunnel back into the superconducting material element 104. Some quasiparticles may escape / tunnel from the first superconducting material layer 108 to the superconducting material element 104 at an escape rate rssc.
[0098] Quasiparticles present in the superconducting material layer 108 having energies lower than the superconducting energy gap A2 Of the superconducting material element 104 are not capable of escaping to the superconducting material element 104 (illustrated by the x- marked arrow). Due to the superconducting energy gap Ai of the first superconducting material layer 108 being smaller than the superconducting energy gap A2 of the superconducting material element 104, a significant portion of quasiparticles are prohibited from escaping or tunneling back to the superconducting material element 104.
[0099] The broadening of the DOS of the first superconducting material layer 108 is a consequence of the proximity effect arising from the first superconducting material layer 108 being connected to the trapping material layer 118 via a tunneling layer 116. The proximity effect is usually considered as a detrimental phenomenon, but in connection with the present invention, gives a beneficial effect. The proximity effect is described for example in A. Hosseinkhani and G. Catelani, Phys. Rev. B 97, 054513 (2018).
[0100] The proximity effect also results in a reduction of the superconducting energy gap A1 of the first superconducting material layer 108, so that the gap A1 is smaller than the superconducting energy gap A2 of the superconducting material element 104. This reduction in gap A1 may take place within the whole first superconducting material layer 108, at least if the first superconducting material layer 108 is relatively thin. The superconducting energy gap A1 may vary along the thickness of the material, with the energy gap being suppressed / reduced to a varying degree.
[0101] For example, if the superconducting material layer 108 is made of the same material as the superconducting material element 104, the proximity effect coming from the presence of the trapping material layer 118 in a tunneling distance, via the tunneling layer 116, of the first superconducting material layer 108 will result in a lowering of the superconducting energy gap of the first superconducting material layer 108 so that A1 is smaller than A2, even though these superconducting gaps would be essentially equivalent without the presence of the trapping material layer 118.
[0102] Through the llsadel theory of superconductivity, the coupling strength of the interface between the first superconducting material layer 108 and the trapping material layer 118 may be characterized via the dimensionless quantity T I-L , in which Here vsis the density of states at the Fermi level of the material of the first superconducting material layer 108, d is the thickness of the first superconducting material layer 108, R "tis the interface resistance between the first superconducting material layer 108 and the trapping material layer 118 and A is an area of the interface.
[0103] The density of states n(e) and the superconducting gap A2may be found by numerical self- consistent solution of the llsadel equation. However, if the coupling strength may be considered as weak, i.e. T^» 1, approximate solutions from the llsadel theory can be formulated as: and where A? is the superconducting energy gap of the first superconducting material layer 108 in the absence of the proximity effect.
[0104] Equations (2) and (3) then show the broadening of the DOS and the lowering of the superconducting energy gap A, of the superconducting material layer 108 that follow from the proximity effect and weak coupling between the first superconducting material layer 108 and the trapping material layer 118. The form of the modified density of states n(e) then follows the well-known phenomenological Dynes form. It may be noted that the density of states approaches the BCS relation once the interface resistance becomes very large so that the proximity effect becomes negligible,
[0105] T — > co,
[0106] The above approximate solutions are valid for structures comprising a normal conductivity metal material as the trapping material for the trapping material layer 118. Similar considerations, however, regarding e.g. the proximity effect are valid also considering trapping material layers 118 comprising a superconducting material having a superconducting bandgap that is lower than a bandgap of the first superconducting material layer 108.
[0107] With the invention, using a SISIN structure or SISIS structure compared to a prior art SIN structure comprising only a trapping material layer separated from the superconducting device’s superconducting material portion, a net trapping rate of quasiparticle of the multilayer structure may be improved by e.g. 40%. As an example, the 40% improvement was obtained for the following SISIN structure. Namely aluminium was used as the superconductor material for the first superconducting material layer 108 and the superconducting element 104 with an energy gap of 180 p.eV. The thickness of the normal metal trap layer 118, of the first superconducting material layer 108 and of the superconducting element 104 is of the order of 80nm. The resistance at the interface between the first superconducting material layer 108 and the trapping material layer 118, thus of the tunneling layer 116 is of the order of 5 Q, 'pm2. The resistance of the first insulating layer 114 between the superconductor layers, thus at the interface between the first superconducting material layer 108 and the superconducting element 104 is around 430 D / pm2. The density of states at the Fermi level of the material of the first superconducting material layer 108 vsand of the trapping material layer 118 vNare of the order of 0,73x1047J'1xrrr3. Finally, the quasiparticles have a Fermi-Dirac distribution with an effective temperature of 50mK.
[0108] Some possible approximate values of superconducting energy gaps A2 or Ai (or A?) that may be provided and which depend on the superconducting material used in the superconducting device, are 180 peV (aluminium), 800 peV (niobium), 380 peV (tantalum), and 1390 peV (niobium nitride).
[0109] The proximity effect may also affect the first superconducting material layer 108 through the presence of the superconducting material element 104. The presence of an insulating layer 114 or tunneling layer 116 between the materials reduces the proximity effect. With a tunneling layer 116 being provided that has a lower resistance than the insulating layer 114, the proximity effect on the first superconducting material layer 108 due to the trapping material layer 118 may still be stronger than the proximity effect on the first superconducting material layer 108 due to the superconducting material layer 104.
[0110] Figure 3 shows at 3A-3C examples of a superconducting apparatus 300 or at least a portion thereof according to embodiments of the invention.
[0111] In all the figures 3A to 3C, the superconducting apparatus 300 comprises more than one superconducting material element 104, in particular here two superconducting material elements 104. However, a superconducting apparatus 300 may also comprise further constituents not depicted in the figures.
[0112] Fig. 3A shows a “top” view of an apparatus 300, as depicted from a viewing angle above a substrate 002. Fig. 3B shows a view through a cross-section AA, depicting also the trapping material layer 118, the tunneling layer 116, the superconducting material layer 108, the insulating layer 114, and substrate 002. Figs. 3A and 3B shown an example of an apparatus 300 where each superconducting material element 104 is provided with one multi-layer structure 102, while Fig. 3C shows an example of an apparatus 300 where each superconducting material element 104, is connected with two multi-layer structures 102. The number of superconducting material elements 104 and multi-layer structures 102 is exemplary.
[0113] A superconducting apparatus 300 may comprise a plurality of multi-layer structures 102 and one superconducting device 106. A superconducting apparatus may also comprise a plurality of multi-layer structures 102 coupled to a plurality of superconducting devices 106.
[0114] Yet, a superconducting apparatus 300 may comprise further components and / or be part of a superconducting arrangement, such as quantum computing device. In one embodiment, a quantum computing device may comprise a plurality of superconducting devices 106 that are quantum devices, such as qubit devices.
[0115] The superconducting apparatus 300 of Figs. 3A-3C may correspond to a structure for providing a superconducting qubit, such as a transmon. The superconducting device 106 may be a qubit device that is provided separately from the multi-layer structure(s) 102. The superconducting apparatus 300 may also be manufactured with the shown constituents to provide a qubit device comprising one or more trap structures, namely one or more multilayer structures.
[0116] Here, the superconducting device 106 comprises at least two superconducting material elements 104, which together may form at least part of one Josephson junction 302. The superconducting material elements 104 may comprise capacitor pads for a qubit structure. The Josephson junction 302 may be provided to couple the various superconducting material elements 104 of the superconducting device 106, where an interface is provided between two superconducting materials, such that the superconducting materials are separated by an insulating layer. The Josephson junction 302 could be provided by the superconducting material elements 104 comprising a plurality of elements e.g. comprising different dimensions or the superconducting material elements 104 may be considered to be coupled through further superconducting material portions, which form the interface of the Josephson junction 302.
[0117] The superconducting material elements 104 may be provided in connection with at least one multi-layer structure 102. Each superconducting material element 104 may be provided in connection with a differing number of multi-layer structures 102. Some superconducting material elements 104 may be provided with no multi-layer structure 102. Each of the multilayer structures 102 may be identical or they may vary, e.g. in terms of dimensions or properties of the layer materials.
[0118] A thickness f of a superconducting material element 104 may be 35-250 pm. A length I of a superconducting material element 104 may be 80-500 pm.
[0119] At least one multi-layer structure 102 may be provided in connection with a superconducting material element 104 such that a distance from the multi-layer structure 102 to a Josephson junction 302 is 5 to 10 times the coherence length of the superconducting material of the superconducting element of the superconducting device. For example, when aluminium is used as superconducting material, the distance from the multi-layer structure to a Josephson junction may be in the range of 10-50 pm, preferably 20-40 pm.
[0120] A larger entity or device, such as a quantum computing device, may comprise a plurality of superconducting apparatuses 300.
[0121] Figure 4 shows a further illustration of a superconducting apparatus 300, comprising exemplary multi-layer structures 102 according to the invention and a superconducting device 106. The superconducting device 106 comprises two superconducting elements 104, separated from each other by a Josephson Junction 302. A superconducting material element 104 may be provided in connection with a plurality of multi-layer structures 102, with Fig. 4 depicting a case where each of the superconducting material elements 104 is provided in connection with three multi-layer structures 102. The multi-layer structures 102 may be provided next to each other laterally on each superconducting element 104, side- by-side. The multi-layer structures 102 may be provided as evenly spaced or with other selected mutual configuration.
[0122] Figures 5A and 5B show further examples of superconducting apparatuses 300 according to the invention. The superconducting device 106 may be a Xmon qubit device. Figures 5A and 5B depict the structures as viewed from above, from a viewing angle perpendicular to a plane that corresponds to a substrate (not shown) onto which the superconducting device 106 may be provided. The Xmon qubit device may comprise or be coupled to a Josephson junction which may reside at the end of one of the arms.
[0123] Fig. 5A and 5B illustrate a Xmon qubit device, meaning the superconducting element 104 has the shape of a cross, with two arms of same length crossing each other in the center point. A length Li of a side arm of the superconducting element 104 may be about 150 pm. The length L2 of a multi-layer structure 102 may then be about 5 pm. The length L2 corresponds to the width of the multilayer structure in the lateral direction. The dimensions are given as exemplary.
[0124] Fig. 5B shows an embodiment of the invention where a plurality of multi-layer structures 102 are arranged in connection with the superconducting material element 104. Here, a central multi-layer structure 102’ may be provided at the central part of the superconducting material element 104 and generally following the shape of the superconducting material element 104, i.e. the material layers of the central multi-layer structure 102’ in this case may be formed as exhibiting an x shape from the showed viewing angle.
[0125] In addition to the central multi-layer structure 102’ the apparatus 300 may comprise a further multi-layer structure 102 at each of the arms of the superconducting material portion 104. The multi-layer structures 102’, 102 have the same type of vertical structure, namely they comprise the same layers and the same arrangement of layers, being a SISIN structure according to the invention. In an embodiment, the central multi-layer structure 102’ and the other multi-layer structures can have a different type of structure. The central multi-layer structure 102’ and the other multi-layer structure 102 are separated by a distance d in a lateral direction following the direction of the arm of the superconducting element 104. The distance d between the central multi-layer structure 102’ and a further multi-layer structure 102 may be between 60 pm to 90 pm, when the length Li of a side arm is around 150 pm .
[0126] Figure 6 illustrates a flow chart of a method of manufacturing a superconducting apparatus 300 according to an exemplary embodiment of the invention.
[0127] According to the invention, a method of manufacturing a superconducting apparatus 300 comprises providing at least one superconducting device 106 comprising at least a superconducting material element 104 on a substrate 002, and providing at least one multilayer structure 102 on a surface of at least a portion of the superconductor material element 104 of the at least one superconducting device 106.
[0128] A substrate 002 may be provided 602, onto which a superconducting device 106 comprising a superconducting material element 104 may be provided 604. The steps 602 and 604 may also be carried out separately and may not be considered necessary to carry out the invention. A substrate 002 may also be considered to be part of a superconducting device 106 that may be pre-made and obtained before carrying out the providing of at least one multi-layer structure 102 according to the present invention.
[0129] At 606, providing at least one multi-layer structure comprises providing at least one (first) insulating layer 114 on a surface 106a of the superconducting device 106. The insulating layer 114 may be fabricated onto the surface 106a of the superconducting device 106 using suitable deposition techniques, like plasma deposition-based techniques, atomic layer deposition or oxidation techniques. The providing of the insulating layer may comprise deposition of an oxide layer as the insulating layer, or the successive deposition of various oxide layers, of the same oxide material or different oxide materials. The insulating layer 114 may also be a native oxide layer grown on the surface 106a of the superconducting device 106.
[0130] In addition to the provision 606 of the insulating layer 114, the providing of the multi-layer structure 102 comprises providing 608 at least one first superconducting layer 108, providing 610 at least one tunneling layer 116, and providing 612 at least one trapping material layer 118. In the method, each successive layer may be fabricated onto a previously provided layer, e.g. using standard materials deposition techniques.
[0131] The providing a multi-layer structure 102 above the surface 106a of the superconducting element 106 results in the insulating layer 114 being sandwiched between the superconducting element 104 of the superconducting device and the superconducting material layer 108 of the multi-layer structure 102. The insulating layer 114 is the layer connecting the multi-layer structure 102 with the superconducting device 106.
[0132] In the variant where the at least one tunneling layer 116 is a second insulating layer, such layer can be provided by standard oxide deposition techniques, as for the providing of the first insulating layer 114. The second insulating layer 116 can also be a native oxide layer which has grown on the first superconducting layer 108. Above this native oxide layer 116 is then deposited a trapping layer 118, being either a normal-conductivity metal layer 118 or a superconducting material layer 118.
[0133] According to the method of fabrication, all the layers of the multi-layer structure are positioned on the same side of the superconducting device 106. All the layers of the multilayer structure 102, namely the at least one insulating layer 114, the at least one first superconducting layer 108, the at least one tunneling layer 116, and the at least one trapping material layer 118 are provided on one side of the superconducting device 106, on the same side. The side of the superconducting device 106 where all the layers of the multilayer structure are provided is the side of the superconducting device where the superconducting element 104 is provided. On the figures, the side corresponds to the surface 106a of the superconducting device 106.
[0134] In some embodiments of the method of manufacturing a superconducting apparatus 300, the step of providing at least one multi-layer structure 102 may comprise providing more than one multi-layer structure 102. The multi-layer structures 102 may be provided side-by- side on at least one of the at least one superconducting devices 106, in particular on the superconducting material element 104 of at least one of the at least one superconducting devices 106. The multi-layer structures 102 may be provided separately and at separate times or they may be fabricated onto at least one or onto a plurality of superconducting devices simultaneously.
[0135] In one example, a superconducting apparatus 300 may form at least part of a quantum processing unit, comprising at least a plurality of qubits as superconducting devices 106. Here, one or a plurality of the qubits may each be provided with one or more multilayer structures 102.
[0136] As a result of the method of fabricating a superconducting apparatus according to the invention, at least one structure corresponding to a superconducting-insulating- superconducting-insulating-metal, namely a SISIN structure (or superconducting-insulating- superconducting-insulating-superconducting, SISIS), has been fabricated in a superconducting apparatus 300. The at least one SISIN or SISIS structure comprised in the superconducting apparatus 300 enables to reduce the density of quasiparticles present in the superconducting layers of the superconducting apparatus, thus improving the superconducting apparatus 300 compared to the use of state of the art SN, superconductormetal, or SIN, superconductor-insulator-metal, structures for trapping quasiparticles within a superconducting apparatus.
[0137] The invention has been explained above with reference to the aforementioned embodiments, and several advantages of the invention have been demonstrated. It is clear that the invention is not only restricted to these embodiments, but comprises all possible embodiments within the spirit and scope of inventive thought and the following patent claims.
[0138] The features recited in dependent claims are mutually freely combinable unless otherwise explicitly stated.
Claims
CLAIMS1. A multi-layer structure (102) to reduce quasiparticle density in a superconducting device (106), said multi-layer structure (102) being configured to be coupled to a superconducting device, wherein the multi-layer structure (102) comprises at least a first superconducting material layer (108), at least one trapping material layer (118), at least one insulating layer (114), and at least one tunneling layer (116), wherein the tunneling layer (116) is provided between the trapping material layer (118) and the first superconducting material layer (108), characterized in that the multi-layer structure (102) is configured to be coupled to the superconducting device (106) via the insulating layer (114) such that the insulating layer (114) is provided between the superconducting device (106) and the first superconducting material layer (108).
2. The multi-layer structure (102) of claim 1 , wherein a thickness of the tunneling layer (116) is inferior to a thickness of the insulating layer (114).
3. The multi-layer structure (102) of any one of claims 1 or 2, wherein a resistance of the tunneling layer (116) is configured to be lower than a resistance of the insulating layer (114), preferably 1 to 2 orders of magnitude lower.
4. The multi-layer structure (102) of any previous claim, wherein the at least one trapping material layer (118) comprises a normal-conductivity metal material and / or a superconducting material, said superconducting material having a lower superconducting energy gap A3 than the superconducting material of the first superconducting material layer (108).
5. The multi-layer structure (102) of any previous claim, wherein the first superconducting material layer (108) is configured to provide a superconducting energy gap A1 that is smaller than a superconducting energy gap A2 of a superconducting material element (104) of the superconducting device (106) that is configured to be coupled to the multi-layer structure (102).
6. The multi-layer structure (102) of any previous claim, wherein the first superconducting material layer (108) comprises the same superconducting material as the superconducting material element (104) of the superconducting device (106).
7. The multi-layer structure (102) of any previous claim, wherein a thickness of the at least first superconducting material layer (108) and / or a thickness of the trapping material layer (118) is comprised between 20 to 500 nm, preferably between 80 to 200 nm.
8. A superconducting apparatus (300) comprisingat least one superconducting device (106) comprising at least a superconducting material element (104), and at least one multi-layer structure (102) of any of claims 1-7, wherein the at least one multi-layer structure (102) is coupled to the at least one superconducting device (106), in particular to the superconducting material element (104) of the at least one superconducting device (106), more in particular to a portion of the superconducting material element (104), via the insulating layer (114).
9. The superconducting apparatus (300) of claim 8, wherein the insulating layer (114) of the at least one multi-layer structure (102) is sandwiched between the at least first superconducting material layer (108) and the superconducting material element (104).
10. The superconducting apparatus (300) of previous claim 8 or 9, wherein the multilayer structure (102) is configured to provide a tunneling rate of quasiparticles from the at least first superconducting material layer (108) to the trapping material layer (118) that is superior to a tunneling rate of quasiparticles from the superconducting device (106) to the at least first superconducting material layer (108) of the multilayer structure (102).
11. The superconducting apparatus (300) of any of previous claims 8-10, wherein the multi-layer structure (102) is configured to reduce a tunneling rate of quasiparticles from the trapping material layer (118) to the superconducting device (106).
12. The superconducting apparatus (300) of any of previous claims 8-11 , wherein the multi-layer structure (102) is configured to provide a net trapping rate of quasiparticles that is higher than the net trapping rate of quasiparticles of a trapping material layer (118) coupled to a superconducting device (106), such that the tunneling of quasiparticles from the trapping material layer (118) to the at least first superconducting layer (108) is reduced.
13. The superconducting apparatus (300) of any one of claims 8-12, wherein said at least one superconducting device (106) comprises or is connectable to at least one Josephson junction (302).
14. The superconducting apparatus (300) of claim 13, wherein the at least one multilayer structure (102) is positioned adjacent to the Josephson junction along a longitudinal axis of the superconducting device (106), preferably such that a distance between the multi-layer structure (102) and the Josephson junction (302) is 5 to 10 times the coherence length of the superconducting material of the superconducting element (104) of the superconducting device (106).
15. The superconducting apparatus (300) of claims 8 to 14, comprising a plurality of multi-layer structures (102) provided next to each other laterally on at least one of the at least one superconducting device (106), in particular a plurality of multi-layer structures (102) according to any of claims 1-7.
16. A method of manufacturing a superconducting apparatus (300) according to any one of claims 8 to 15, the method comprising: providing at least one superconducting device (106) comprising at least a superconducting material element (104) on a substrate (002), and providing at least one multi-layer structure (102) according to any one of claims 1 to 7, characterized in that the at least one multi-layer structure (102) is provided on a surface (106a) of the at least one superconducting device (106).
17. The method according to claim 16, wherein the step of providing the at least one multi-layer structure (102) comprises a step of providing an insulating layer (114) on at least a portion of a superconducting material element (104) of the at least one superconducting device (106).
18. The method according to any of claims 16 or 17, wherein the step of providing the at least one multi-layer structure (102) comprises providing all the layers of the multilayer structure (102) on the same side of the superconducting device (106), in particular the side of the superconducting device (106) where the superconducting element (104) is provided.
19. The method according to any of claims 16 to 18, wherein the step of providing at least one multi-layer structure (102) comprises providing more than one multi-layer structure (102), wherein the multi-layer structures (102) are provided side-by-side on at least one of the at least one superconducting device (106), in particular on the superconducting material element (104) of at least one of the at least one superconducting devices (106).