Induced Superconducting Gap Research Articles

Direct Microwave Spectroscopy of Andreev Bound States in Planar Ge Josephson Junctions

We demonstrate microwave measurements of the Andreev-bound-state (ABS) spectrum in planar Josephson junctions (JJs) defined in Ge high-mobility two-dimensional hole gases contacted by superconducting platinum germanosilicide (PtSiGe). The JJs and readout circuitry are located on separate chips and inductively coupled via flip-chip bonding. For a device with 350-nm junction length, the spectroscopic signatures were consistent with the short-junction limit, with an induced superconducting gap Δ∗≈48μeV and transmission τ≈0.94. The interaction between the highest-transmission ABS and the resonator was well described by a Jaynes-Cummings model with a vacuum Rabi splitting of approximately 6 MHz. A device with a junction length of 1μm showed an ABS spectrum consistent with a long-junction model. Time-resolved monitoring of the readout resonator in the dispersive regime revealed gate-voltage tunable-junction parity fluctuations on the time scale of seconds. Our work indicates a viable path toward hybrid quantum devices based on planar Ge. Published by the American Physical Society 2024

Versatile Method of Engineering the Band Alignment and the Electron Wavefunction Hybridization of Hybrid Quantum Devices.

Hybrid devices that combine superconductors (S) and semiconductors (Sm) have attracted great attention due to the integration of the properties of both materials, which relies on the interface details and the resulting coupling strength and wavefunction hybridization. However, until now, none of the experiments have reported good control of the band alignment of the interface, as well as its tunability to the coupling and hybridization. Here, the interface is modified by inducing specific argon milling while maintaining its high quality, e.g., atomic connection, which results in a large induced superconducting gap and ballistic transport. By comparing with Schrödinger-Poisson calculations, it is proven that this method can vary the band bending/coupling strength and the electronic spatial distribution. In the strong coupling regime, the coexistence and tunability of crossed Andreev reflection and elastic co-tunneling-key ingredients for the Kitaev chain-are confirmed. This method is also generic for other materials and achieves a hard and huge superconducting gap in lead and indium antimonide nanowire (Pb-InSb) devices. Such a versatile method, compatible with the standard fabrication process and accompanied by the well-controlled modification of the interface, will definitely boost the creation of more sophisticated hybrid devices for exploring physics in solid-state systems.

Hard Superconducting Gap in PbTe Nanowires

Semiconductor nanowires coupled to a superconductor provide a powerful testbed for quantum device physics such as Majorana zero modes and gate-tunable hybrid qubits. The performance of these quantum devices heavily relies on the quality of the induced superconducting gap. A hard gap, evident as vanishing subgap conductance in tunneling spectroscopy, is both necessary and desired. A hard gap has been achieved and extensively studied before in III–V semiconductor nanowires (InAs and InSb). In this study, we present the observation of a hard superconducting gap in PbTe nanowires coupled to a superconductor Pb. The gap size Δ is ∼ 1 meV (maximally 1.3 meV in one device). Additionally, subgap Andreev bound states can also be created and controlled through gate tuning. Tuning a device into the open regime can reveal Andreev enhancement of the subgap conductance. These results pave the way for diverse superconducting quantum devices based on PbTe nanowires.

Andreev Reflection and Klein Tunneling in High-Temperature Superconductor-Graphene Junctions.

Scattering processes in quantum materials emerge as resonances in electronic transport, including confined modes, Andreev states, and Yu-Shiba-Rusinov states. However, in most instances, these resonances are driven by a single scattering mechanism. Here, we show the appearance of resonances due to the combination of two simultaneous scattering mechanisms, one from superconductivity and the other from graphene p-n junctions. These resonances stem from Andreev reflection and Klein tunneling that occur at two different interfaces of a hole-doped region of graphene formed at the boundary with superconducting graphene due to proximity effects from Bi_{2}Sr_{2}Ca_{1}Cu_{2}O_{8+δ}. The resonances persist with gating from p^{+}-p and p-n configurations. The suppression of the oscillation amplitude above the bias energy which is comparable to the induced superconducting gap indicates the contribution from Andreev reflection. Our experimental measurements are supported by quantum transport calculations in such interfaces, leading to analogous resonances. Our results put forward a hybrid scattering mechanism in graphene-high-temperature superconductor heterojunctions of potential impact for graphene-based Josephson junctions.

Hard superconducting gap in germanium

The co-integration of spin, superconducting, and topological systems is emerging as an exciting pathway for scalable and high-fidelity quantum information technology. High-mobility planar germanium is a front-runner semiconductor for building quantum processors with spin-qubits, but progress with hybrid superconductor-semiconductor devices is hindered by the difficulty in obtaining a superconducting hard gap, that is, a gap free of subgap states. Here, we address this challenge by developing a low-disorder, oxide-free interface between high-mobility planar germanium and a germanosilicide parent superconductor. This superconducting contact is formed by the thermally-activated solid phase reaction between a metal, platinum, and the Ge/SiGe semiconductor heterostructure. Electrical characterization reveals near-unity transparency in Josephson junctions and, importantly, a hard induced superconducting gap in quantum point contacts. Furthermore, we demonstrate phase control of a Josephson junction and study transport in a gated two-dimensional superconductor-semiconductor array towards scalable architectures. These results expand the quantum technology toolbox in germanium and provide new avenues for exploring monolithic superconductor-semiconductor quantum circuits towards scalable quantum information processing.

InAs/MoRe Hybrid Semiconductor/Superconductor Nanowire Devices

Implementing superconductors capable of proximity-inducing a large energy gap in semiconductors in the presence of strong magnetic fields is a major goal toward applications of semiconductor/superconductor hybrid materials in future quantum information technologies. Here, we study the performance of devices consisting of InAs nanowires in electrical contact with molybdenum-rhenium (MoRe) superconducting alloys. The MoRe thin films exhibit transition temperatures of ∼10 K and critical fields exceeding 6 T. Normal/superconductor devices enabled tunnel spectroscopy of the corresponding induced superconductivity, which was maintained up to ∼10 K, and MoRe-based Josephson devices exhibited supercurrents and multiple Andreev reflections. We determine an induced superconducting gap lower than expected from the transition temperature and observe gap softening at finite magnetic field. These may be common features for hybrids based on large-gap, type II superconductors. The results encourage further development of MoRe-based hybrids.

In Situ Epitaxy of Pure Phase Ultra-Thin InAs-Al Nanowires for Quantum Devices

We demonstrate the in situ growth of ultra-thin InAs nanowires with an epitaxial Al film by molecular-beam epitaxy. Our InAs nanowire diameter (∼30 nm) is much thinner than before (∼100 nm). The ultra-thin InAs nanowires are pure phase crystals for various different growth directions. Transmission electron microscopy confirms an atomically abrupt and uniform interface between the Al shell and the InAs wire. Quantum transport study on these devices resolves a hard induced superconducting gap and 2e-periodic Coulomb blockade at zero magnetic field, a necessary step for future Majorana experiments. By reducing wire diameter, our work presents a promising route for reaching fewer sub-band regime in Majorana nanowire devices.

Evidence for spin-polarized bound states in semiconductor–superconductor–ferromagnetic-insulator islands

We report Coulomb blockade transport studies of semiconducting InAs nanowires grown with epitaxial superconducting Al and ferromagnetic insulator EuS on overlapping facets. Comparing experiment to a theoretical model, we associate cotunneling features in even-odd bias spectra with spin-polarized Andreev levels. Results are consistent with zero-field spin splitting exceeding the induced superconducting gap. Energies of subgap states are tunable on either side of zero via electrostatic gates.

Superconductivity and Parity Preservation in As-Grown In Islands on InAs Nanowires.

We report in situ synthesis of crystalline indium islands on InAs nanowires grown by molecular beam epitaxy. Structural analysis by transmission electron microscopy showed that In crystals grew in a tetragonal body-centered crystal structure within two families of orientations relative to wurtzite InAs. The crystalline islands had lengths < 500 nm and low-energy surfaces, suggesting that growth was driven mainly by surface energy minimization. Electrical transport through In/InAs devices exhibited Cooper pair charging, evidencing charge parity preservation and a pristine In/InAs interface, with an induced superconducting gap ∼ 0.45 meV. Cooper pair charging persisted to temperatures > 1.2 K and magnetic fields ∼ 0.7 T, demonstrating that In/InAs hybrids belong to an expanding class of semiconductor/superconductor hybrids operating over a wider parameter space than state-of-the-art Al-based hybrids. Engineering crystal morphology while isolating single islands using shadow epitaxy provides an interesting alternative to previous semiconductor/superconductor hybrid morphologies and device geometries.

InSbAs Two-Dimensional Electron Gases as a Platform for Topological Superconductivity.

Topological superconductivity can be engineered in semiconductors with strong spin-orbit interaction coupled to a superconductor. Experimental advances in this field have often been triggered by the development of new hybrid material systems. Among these, two-dimensional electron gases (2DEGs) are of particular interest due to their inherent design flexibility and scalability. Here, we discuss results on a 2D platform based on a ternary 2DEG (InSbAs) coupled to in situ grown aluminum. The spin-orbit coupling in these 2DEGs can be tuned with the As concentration, reaching values up to 400 meV Å, thus exceeding typical values measured in its binary constituents. In addition to a large Landé g-factor of ∼55 (comparable to that of InSb), we show that the clean superconductor-semiconductor interface leads to a hard induced superconducting gap. Using this new platform, we demonstrate the basic operation of phase-controllable Josephson junctions, superconducting islands, and quasi-1D systems, prototypical device geometries used to study Majorana zero modes.

Electrical Properties of Selective-Area-Grown Superconductor-Semiconductor Hybrid Structures on Silicon

We present a superconductor-semiconductor material system that is both scalable and monolithically integrated on a silicon substrate. It uses selective area growth of Al-InAs hybrid structures on a planar III-V buffer layer, grown directly on a high resistivity silicon substrate. We characterized the electrical properties of this material system at millikelvin temperatures and observed a high average field-effect mobility of $\mu \approx 3200\,\mathrm{cm^2/Vs}$ for the InAs channel, and a hard induced superconducting gap. Josephson junctions exhibited a high interface transmission, $\mathcal{T} \approx 0.75 $, gate voltage tunable switching current with a product of critical current and normal state resistance, $I_{\mathrm{C}}R_{\mathrm{N}} \approx 83\,\mathrm{\mu V}$, and signatures of multiple Andreev reflections. These results pave the way for scalable and high coherent gate voltage tunable transmon devices and other superconductor-semiconductor hybrids fabricated directly on silicon.

Shadow-wall lithography of ballistic superconductor\u2013semiconductor quantum devices

The realization of hybrid superconductor–semiconductor quantum devices, in particular a topological qubit, calls for advanced techniques to readily and reproducibly engineer induced superconductivity in semiconductor nanowires. Here, we introduce an on-chip fabrication paradigm based on shadow walls that offers substantial advances in device quality and reproducibility. It allows for the implementation of hybrid quantum devices and ultimately topological qubits while eliminating fabrication steps such as lithography and etching. This is critical to preserve the integrity and homogeneity of the fragile hybrid interfaces. The approach simplifies the reproducible fabrication of devices with a hard induced superconducting gap and ballistic normal-/superconductor junctions. Large gate-tunable supercurrents and high-order multiple Andreev reflections manifest the exceptional coherence of the resulting nanowire Josephson junctions. Our approach enables the realization of 3-terminal devices, where zero-bias conductance peaks emerge in a magnetic field concurrently at both boundaries of the one-dimensional hybrids.

Enhanced Proximity Effect in Zigzag-Shaped Majorana Josephson Junctions

High density superconductor-semiconductor-superconductor junctions have a small induced superconducting gap due to the quasiparticle trajectories with a large momentum parallel to the junction having a very long flight time. Because a large induced gap protects Majorana modes, these long trajectories constrain Majorana devices to a low electron density. We show that a zigzag-shaped geometry eliminates these trajectories, allowing the robust creation of Majorana states with both the induced gap E_{gap} and the Majorana size ξ_{M} improved by more than an order of magnitude for realistic parameters. In addition to the improved robustness of Majoranas, this new zigzag geometry is insensitive to the geometric details and the device tuning.

Erasing odd-parity states in semiconductor quantum dots coupled to superconductors

Quantum dots are gate-defined within InSb nanowires, in proximity to NbTiN superconducting contacts. As the coupling between the dot and the superconductor is increased, the odd-parity occupations become non-discernible (erased) both above and below the induced superconducting gap. Above the gap, conductance in the odd Coulomb valleys increases until the valleys are lifted. Below the gap, Andreev bound states undergo quantum phase transitions to singlet ground states at odd occupancy. We observe that the apparent erasure of odd-parity regimes coincides at low-bias and at high-bias. This observation is reproduced in numerical renormalization group simulations, and is explained qualitatively by a competition between Kondo temperature and the induced superconducting gap. In the erased odd-parity regime, the quantum dot exhibits transport features similar to a finite-size Majorana nanowire, drawing parallels between even-odd dot occupations and even-odd one-dimensional subband occupations.

Hard Superconducting Gap and Diffusion-Induced Superconductors in Ge–Si Nanowires

We show a hard superconducting gap in a Ge–Si nanowire Josephson transistor up to in-plane magnetic fields of 250 mT, an important step toward creating and detecting Majorana zero modes in this system. A hard gap requires a highly homogeneous tunneling heterointerface between the superconducting contacts and the semiconducting nanowire. This is realized by annealing devices at 180 °C during which aluminum interdiffuses and replaces the germanium in a section of the nanowire. Next to Al, we find a superconductor with lower critical temperature (TC = 0.9 K) and a higher critical field (BC = 0.9–1.2 T). We can therefore selectively switch either superconductor to the normal state by tuning the temperature and the magnetic field and observe that the additional superconductor induces a proximity supercurrent in the semiconducting part of the nanowire even when the Al is in the normal state. In another device where the diffusion of Al rendered the nanowire completely metallic, a superconductor with a much higher critical temperature (TC = 2.9 K) and critical field (BC = 3.4 T) is found. The small size of these diffusion-induced superconductors inside nanowires may be of special interest for applications requiring high magnetic fields in arbitrary direction.

Semiconductor-Ferromagnetic Insulator-Superconductor Nanowires: Stray Field and Exchange Field.

Nanowires can serve as flexible substrates for hybrid epitaxial growth on selected facets, allowing for the design of heterostructures with complex material combinations and geometries. In this work we report on hybrid epitaxy of freestanding vapor-liquid-solid grown and in-plane selective area grown semiconductor-ferromagnetic insulator-superconductor (InAs/EuS/Al) nanowire heterostructures. We study the crystal growth and complex epitaxial matching of wurtzite and zinc-blende InAs/rock-salt EuS interfaces as well as rock-salt EuS/face-centered cubic Al interfaces. Because of the magnetic anisotropy originating from the nanowire shape, the magnetic structure of the EuS phase is easily tuned into single magnetic domains. This effect efficiently ejects the stray field lines along the nanowires. With tunnel spectroscopy measurements of the density of states, we show that the material has a hard induced superconducting gap, and magnetic hysteretic evolution which indicates that the magnetic exchange fields are not negligible. These hybrid nanowires fulfill key material requirements for serving as a platform for spin-based quantum applications, such as scalable topological quantum computing.

Floquet second-order topological superconductor driven via ferromagnetic resonance

We consider a Floquet triple-layer setup composed of a two-dimensional electron gas with spin-orbit interactions, proximity coupled to an s-wave superconductor and to a ferromagnet driven at resonance. The ferromagnetic layer generates a time-oscillating Zeeman field which competes with the induced superconducting gap and leads to a topological phase transition. The resulting Floquet states support a second-order topological superconducting phase with a pair of localized zero-energy Floquet Majorana corner states. Moreover, the phase diagram comprises a Floquet helical topological superconductor, hosting a Kramers pair of Majorana edge modes protected by an effective time-reversal symmetry, as well as a gapless Floquet Weyl phase. The topological phases are stable against disorder and parameter variations and are within experimental reach.

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

To form a coherent quantum transport in hybrid superconductor-semiconductor (S-Sm) junctions, the formation of a homogeneous and barrier-free interface between two different materials is necessary. The S-Sm junction with high interface transparency will then facilitate the observation of the induced hard superconducting gap, which is the key requirement to access the topological phases (TPs) and observation of exotic quasiparticles such as Majorana zero modes (MZM) in hybrid systems. A material platform that can support observation of TPs and allows the realization of complex and branched geometries is therefore highly demanding in quantum processing and computing science and technology. Here, we introduce a two-dimensional material system and study the proximity induced superconductivity in semiconducting two-dimensional electron gas (2DEG) that is the basis of a hybrid quantum integrated circuit (QIC). The 2DEG is a 30 nm thick In0.75Ga0.25As quantum well that is buried between two In0.75Al0.25As barriers in a heterostructure. Niobium (Nb) films are used as the superconducting electrodes to form Nb- In0.75Ga0.25As -Nb Josephson junctions (JJs) that are symmetric, planar and ballistic. Two different approaches were used to form the JJs and QICs. The long junctions were fabricated photolithographically, but e-beam lithography was used for short junctions’ fabrication. The coherent quantum transport measurements as a function of temperature in the presence/absence of magnetic field B are discussed. In both device fabrication approaches, the proximity induced superconducting properties were observed in the In0.75Ga0.25As 2DEG. It was found that e-beam lithographically patterned JJs of shorter lengths result in observation of induced superconducting gap at much higher temperature ranges. The results that are reproducible and clean suggesting that the hybrid 2D JJs and QICs based on In0.75Ga0.25As quantum wells could be a promising material platform to realize the real complex and scalable electronic and photonic quantum circuitry and devices.

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform.

To form a coherent quantum transport in hybrid superconductor-semiconductor (S-Sm) junctions, the formation of a homogeneous and barrier-free interface between two different materials is necessary. The S-Sm junction with high interface transparency will then facilitate the observation of the induced hard superconducting gap, which is the key requirement to access the topological phases (TPs) and observation of exotic quasiparticles such as Majorana zero modes (MZM) in hybrid systems. A material platform that can support observation of TPs and allows the realization of complex and branched geometries is therefore highly demanding in quantum processing and computing science and technology. Here, we introduce a two-dimensional material system and study the proximity induced superconductivity in semiconducting two-dimensional electron gas (2DEG) that is the basis of a hybrid quantum integrated circuit (QIC). The 2DEG is a 30 nm thick In0.75Ga0.25As quantum well that is buried between two In0.75Al0.25As barriers in a heterostructure. Niobium (Nb) films are used as the superconducting electrodes to form Nb- In0.75Ga0.25As -Nb Josephson junctions (JJs) that are symmetric, planar and ballistic. Two different approaches were used to form the JJs and QICs. The long junctions were fabricated photolithographically, but e-beam lithography was used for short junctions' fabrication. The coherent quantum transport measurements as a function of temperature in the presence/absence of magnetic field B are discussed. In both device fabrication approaches, the proximity induced superconducting properties were observed in the In0.75Ga0.25As 2DEG. It was found that e-beam lithographically patterned JJs of shorter lengths result in observation of induced superconducting gap at much higher temperature ranges. The results that are reproducible and clean suggesting that the hybrid 2D JJs and QICs based on In0.75Ga0.25As quantum wells could be a promising material platform to realize the real complex and scalable electronic and photonic quantum circuitry and devices.

Superconductivity in twisted graphene NbSe2 heterostructures

We study the low-energy electronic structure of heterostructures formed by one sheet of graphene placed on a monolayer of ${\rm NbSe_2}$. We build a continuous low-energy effective model that takes into account the presence of a twist angle between graphene and ${\rm NbSe_2}$, and of spin-orbit coupling and superconducting pairing in ${\rm NbSe_2}$. We obtain the parameters entering the continuous model via ab-initio calculations. We show that despite the large mismatch between the graphene's and ${\rm NbSe_2}$'s lattice constants, due to the large size of the ${\rm NbSe_2}$'s Fermi pockets, there is a large range of values of twist angles for which a superconducting pairing can be induced into the graphene layer. In addition, we show that the superconducting gap induced into the graphene is extremely robust to an external in-plane magnetic field. Our results show that the size of the induced superconducting gap, and its robustness against in-plane magnetic fields, can be significantly tuned by varying the twist angle.