Proximity-induced Superconductivity Research Articles

Probing electron-hole components of subgap states in Coulomb blockaded Majorana islands

Recent tunneling spectroscopy experiments in semiconducting nanowires with proximity-induced superconductivity have reported robust zero-bias conductance peaks. Such a feature can be compatible with the existence of topological Majorana bound states (MBSs) and with a trivial Andreev bound state (ABS) near zero energy. Here, we argue that additional information, that can distinguish between the two cases, can be extracted from Coulomb-blockade experiments of Majorana islands. The key is the ratio of peak heights of consecutive conductance peaks give information about the electron and hole components of the lowest-energy subgap state. In the MBS case, this ratio goes to one half for long wires, while for short wires with finite MBS overlap it oscillates a function of Zeeman energy with the same period as the MBS energy splitting. We explain how the additional information might help to distinguish a trivial ABS at zero energy from a true MBS and show case examples.

Topological phase detection in Rashba nanowires with a quantum dot

We study theoretically the detection of the topological phase transition occurring in Rashba nanowires with proximity-induced superconductivity using a quantum dot. The bulk states lowest in energy of such a nanowire have a spin polarization parallel or antiparallel to the applied magnetic field in the topological or trivial phase, respectively. We show that this property can be probed by the quantum dot created at the end of the nanowire by external gates. By tuning one of the two spin-split levels of the quantum dot to be in resonance with nanowire bulk states, one can detect the spin polarization of the lowest band via transport measurement. This allows one to determine the topological phase of the Rashba nanowire independently of the presence of Majorana bound states.

Proximity-induced superconductivity within the InAs/GaSb edge conducting state

We experimentally investigate Andreev transport through the interface between an indium superconductor and the edge of the InAs/GaSb bilayer. To cover all possible regimes of InAs/GaSb spectrum, we study samples with 10 nm, 12 nm, and 14 nm thick InAs quantum wells. For the trivial case of a direct band insulator in 10~nm samples, differential resistance demonstrates standard Andreev reflection. For InAs/GaSb structures with band inversion (12~nm and 14 nm samples), we observe distinct low-energy structures, which we regard as direct evidence for the proximity-induced superconductivity within the current-carrying edge state. For 14~nm InAs well samples, we additionally observe mesoscopic-like resistance fluctuations, which are subjected to threshold suppression in low magnetic fields.

Two-band induced superconductivity in single-layer graphene and topological insulator bismuth selenide

Proximity-induced superconductivity in single-layer graphene (SLG) and in topological insulators represent almost ideal examples of superconductivity in two dimensions. Fundamental mechanisms governing superconductivity in the 2D limit are of central interest for modern condensed-matter physics. To deduce fundamental parameters of superconductor/graphene/superconductor and superconductor/bismuth selenide/superconductor junctions we investigate the self-field critical currents in these devices using the formalism of the Ambegaokar–Baratoff model. Our central finding is that the induced superconducting state in SLG and bismuth selenide each exhibits gapping on two superconducting bands. Based on recent results obtained on ultra-thin films of natural superconductors, including single-atomic layer of iron selenide, double and triple atomic layers of gallium, and several atomic layer tantalum disulphide, we conclude that a two-band induced superconducting state in SLG and bismuth selenide is part of a wider, more general multiple-band phenomenology of currently unknown origin.

Multiple odd-frequency superconducting states in buckled quantum spin Hall insulators with time-reversal symmetry

We consider a buckled quantum spin Hall insulator (QSHI), such as silicene, proximity-coupled to a conventional spin-singlet, s-wave superconductor. Even limiting the discussion to the disorder-robust s-wave pairing symmetry, we find both odd-frequency ($\omega$), spin-singlet and spin-triplet pair amplitudes and where both preserve time-reversal symmetry. Our results show that there are two unrelated mechanisms generating these different odd-$\omega$ pair amplitudes. The spin-singlet state is due to the strong inter-orbital processes present in the QSHI. It is exists generically at the edges of the QSHI, but also in the bulk in heavily doped regime if an electric field is applied. The spin-triplet state requires a finite gradient in the proximity-induced superconducting order along the edge, which we find is automatically generated at the atomic scale for armchair edges but not at zigzag edges. In combination these results make superconducting QSHIs a very exciting venue for investigating not only the existence of odd-$\omega$ superconductivity, but also the interplay between different odd-$\omega$ states.

Experimentally accessible topological quality factor for wires with zero energy modes

Spin-orbit coupled semiconducting nanowires with proximity-induced superconductivity are expected to host Majorana zero modes at their endpoints when a sufficiently strong magnetic field is applied. The resulting phase would be a one-dimensional topological superconductor. However, while a variety of experiments have been performed observing a zero bias conductance peak (suggestive of Majorana zero modes), the topological nature of these physical systems is still a subject of debate. Here we suggest a quantitative test of the degree to which a system displaying a zero bias peak may be considered topological. The experiment is similar to previous measurements of conductance, but is performed with the aid of a quantum dot at the wire's end. We arrive at the surprising result that the non-local nature of the topological system may be identified through a local measurement.

Proximity-induced superconductivity in Landau-quantized graphene monolayers

We consider massless Dirac fermions in a graphene monolayer subject to both a perpendicular magnetic field $B$ and a proximity-induced pairing gap $\Delta$. When the chemical potential is at the Dirac point, our exact solution of the Bogoliubov-de Gennes equation yields $\Delta$-independent relativistic Landau levels. Since eigenstates depend on $\Delta$, many observables nevertheless are sensitive to pairing, e.g., the local density of states or the edge state spectrum. By solving the problem with an additional in-plane electric field, we also discuss how snake states are influenced by a pairing gap.

Missing Shapiro steps and the 8π -periodic Josephson effect in interacting helical electron systems

Two-particle backscattering in time-reversal invariant interacting helical electron systems can lead to the formation of quasiparticles with charge $e/2$. We propose a way to detect such states by means of the Josephson effect in the presence of proximity-induced superconductivity. In this case, the existence of $e/2$ charges leads to an $8 \pi$-periodic component of the Josephson current which can be identified through measurement of Shapiro steps in Josephson junctions. In particular, we show that even when there is weak explicit time-reversal symmetry breaking, which causes the two-particle backscattering to be a sub-leading effect at low energies, its presence can still be detected in driven, current-biased Shapiro step measurements. The disappearance of some of these steps as a function of the drive frequency is directly related to the existence of non-Abelian zero-energy states. We suggest that this effect can be measured in current state-of-the-art Rashba wires.

Majorana states in prismatic core-shell nanowires

We consider core-shell nanowires with conductive shell and insulating core and with polygonal cross section. We investigate the implications of this geometry on Majorana states expected in the presence of proximity-induced superconductivity and an external magnetic field. A typical prismatic nanowire has a hexagonal profile, but square and triangular shapes can also be obtained. The low-energy states are localized at the corners of the cross section, i.e., along the prism edges, and are separated by a gap from higher energy states localized on the sides. The corner localization depends on the details of the shell geometry, i.e., thickness, diameter, and sharpness of the corners. We study systematically the low-energy spectrum of prismatic shells using numerical methods and derive the topological phase diagram as a function of magnetic field and chemical potential for triangular, square, and hexagonal geometries. A strong corner localization enhances the stability of Majorana modes to various perturbations, including the orbital effect of the magnetic field, whereas a weaker localization favorizes orbital effects and reduces the critical magnetic field. The prismatic geometry allows the Majorana zero-energy modes to be accompanied by low-energy states, which we call pseudo Majorana, and which converge to real Majoranas in the limit of small shell thickness. We include the Rashba spin-orbit coupling in a phenomenological manner, assuming a radial electric field across the shell.

Multifaceted impact of a surface step on superconductivity in atomically thin films

Recent experiments show that an atomic step on the surface of atomically thin metallic films can strongly affect electronic transport. Here we reveal multiple and versatile effects that such a surface step can have on superconductivity in ultrathin films. By solving the Bogoliubov-de Gennes equations self-consistently in this regime, where quantum confinement dominates the emergent physics, we show that the electronic structure is profoundly modified on the two sides of the step, as is the spatial distribution of the superconducting order parameter and its dependence on temperature and electronic gating. Furthermore, the surface step changes non-trivially the transport properties both in the proximity-induced superconducting order parameter and the Josephson effect, depending on the step height. These results offer a new route to tailor superconducting circuits and design atomically thin hetero-junctions made of one same material.

Publisher's Note: Coupling and braiding Majorana bound states in networks defined in two-dimensional electron gases with proximity-induced superconductivity [Phys. Rev. B 96, 035444 (2017)

Publisher's Note: Coupling and braiding Majorana bound states in networks defined in two-dimensional electron gases with proximity-induced superconductivity [Phys. Rev. B 96, 035444 (2017)

Andreev bound states versus Majorana bound states in quantum dot-nanowire-superconductor hybrid structures: Trivial versus topological zero-bias conductance peaks

Motivated by an important recent experiment [Deng et al., Science 354, 1557 (2016)], we theoretically consider the interplay between Andreev bound states(ABSs) and Majorana bound states(MBSs) in quantum dot-nanowire semiconductor systems with proximity-induced superconductivity(SC), spin-orbit coupling and Zeeman splitting. The dot induces ABSs in the SC nanowire which show complex behavior as a function of Zeeman splitting and chemical potential, and the specific question is whether two such ABSs can come together forming a topological MBS. We consider physical situations involving the dot being non-SC, SC, or partially SC. We find that the ABSs indeed tend to coalesce together producing near-zero-energy midgap states as Zeeman splitting and/or chemical potential are increased, but this mostly happens in the non-topological regime although there are situations where the ABSs could come together forming a topological MBS. The two scenarios(two ABSs forming a near-zero-energy non-topological ABS or a zero-energy topological MBS) are difficult to distinguish by tunneling conductance spectroscopy due to essentially the same signatures. Theoretically we distinguish them by knowing the critical Zeeman splitting for the topological quantum phase transition or by calculating the topological visibility. We find that the "sticking together" propensity of ABSs to produce a zero-energy midgap state is generic in class D systems, and by itself says nothing about the topological nature of the underlying SC nanowire. One must use caution in interpreting tunneling conductance measurements where the midgap sticking-together behavior of ABSs cannot be construed as definitive evidence for topological SC with non-Abelian MBSs. We also suggest some experimental techniques for distinguishing between trivial and topological ZBCPs.

RETRACTED ARTICLE: Epitaxy of advanced nanowire quantum devices

Semiconductor nanowires are ideal for realizing various low-dimensional quantum devices. In particular, topological phases of matter hosting non-Abelian quasiparticles (such as anyons) can emerge when a semiconductor nanowire with strong spin-orbit coupling is brought into contact with a superconductor. To exploit the potential of non-Abelian anyons-which are key elements of topological quantum computing-fully, they need to be exchanged in a well-controlled braiding operation. Essential hardware for braiding is a network of crystalline nanowires coupled to superconducting islands. Here we demonstrate a technique for generic bottom-up synthesis of complex quantum devices with a special focus on nanowire networks with a predefined number of superconducting islands. Structural analysis confirms the high crystalline quality of the nanowire junctions, as well as an epitaxial superconductor-semiconductor interface. Quantum transport measurements of nanowire 'hashtags' reveal Aharonov-Bohm and weak-antilocalization effects, indicating a phase-coherent system with strong spin-orbit coupling. In addition, a proximity-induced hard superconducting gap (with vanishing sub-gap conductance) is demonstrated in these hybrid superconductor-semiconductor nanowires, highlighting the successful materials development necessary for a first braiding experiment. Our approach opens up new avenues for the realization of epitaxial three-dimensional quantum architectures which have the potential to become key components of various quantum devices.

On-Chip Andreev Devices: Hard Superconducting Gap and Quantum Transport in Ballistic Nb-In0.75 Ga0.25 As-Quantum-Well-Nb Josephson Junctions.

A superconducting hard gap in hybrid superconductor-semiconductor devices has been found to be necessary to access topological superconductivity that hosts Majorana modes (non-Abelian excitation). This requires the formation of homogeneous and barrier-free interfaces between the superconductor and semiconductor. Here, a new platform is reported for topological superconductivity based on hybrid Nb-In0.75 Ga0.25 As-quantum-well-Nb that results in hard superconducting gap detection in symmetric, planar, and ballistic Josephson junctions. It is shown that with careful etching, sputtered Nb films can make high-quality and transparent contacts to the In0.75 Ga0.25 As quantum well, and the differential resistance and critical current measurements of these devices are discussed as a function of temperature and magnetic field. It is demonstrated that proximity-induced superconductivity in the In0.75 Ga0.25 As-quantum-well 2D electron gas results in the detection of a hard gap in four out of seven junctions on a chip with critical current values of up to 0.2 µA and transmission probabilities of >0.96. The results, together with the large g-factor and Rashba spin-orbit coupling in In0.75 Ga0.25 As quantum wells, which indeed can be tuned by the indium composition, suggest that the Nb-In0.75 Ga0.25 As-Nb system can be an excellent candidate to achieve topological phase and to realize hybrid topological superconducting devices.

Measuring Majorana nonlocality and spin structure with a quantum dot

Robust zero bias transport anomalies in semiconducting nanowires with proximity-induced superconductivity have been convincingly demonstrated in various experiments. While these are compatible with the existence of Majorana zero modes at the ends of the nanowire, a direct proof of their non-locality and topological protection is now needed. Here we show that a quantum dot at the end of the nanowire may be used as a powerful spectroscopic tool to quantify the degree of Majorana non-locality through a local transport measurement. Moreover, the spin polarization of dot sub-gap states at singlet-doublet transitions in the Coulomb blockade regime allows the dot to directly probe the spin structure of the Majorana wave function, and indirectly measure the spin-orbit coupling of the nanowire.

Coupling and braiding Majorana bound states in networks defined in two-dimensional electron gases with proximity-induced superconductivity

Two-dimensional electron gases with strong spin-orbit coupling covered by a superconducting layer offer a flexible and potentially scalable platform for Majorana networks. We predict Majorana bound states (MBSs) to appear for experimentally achievable parameters and realistic gate potentials in two designs: either underneath a narrow stripe of a superconducting layer (S-stripes) or where a narrow stripe has been removed from a uniform layer (N-stripes). The coupling of the MBSs can be tuned for both types in a wide range (< 1 neV to >10 $\mu$eV) using gates placed adjacent to the stripes. For both types, we numerically compute the local density of states for two parallel Majorana-stripe ends as well as Majorana trijunctions formed in a tuning-fork geometry. The MBS coupling between parallel Majorana stripes can be suppressed below 1 neV for potential barriers in the meV range for separations of about 200 nm. We further show that the MBS couplings in a trijunction can be gate-controlled in a range similar to the intra-stripe coupling while maintaining a sizable gap to the excited states (tens of $\mu$eV). Altogether, this suggests that braiding can carried out on a time scale of 10-100 ns.

Proximity-induced superconductivity in all-silicon superconductor /normal-metal junctions

We have realised laser-doped all-silicon superconducting (S)/ normal metal (N) bilayers of tunable thickness and dopant concentration. We observed a strong reduction of the bilayers critical temperature when increasing the normal metal thickness, a signature of the highly transparent S/N interface associated to the epitaxial sharp laser doping profile. We extracted the interface resistance by fitting with the linearised Usadel equations, demonstrating a reduction of one order of magnitude from previous superconductor/doped Si interfaces. In this well controlled crystalline system we exploited the low resistance S/N interfaces to elaborate all-silicon lateral SNS Josephson junctions with long range proximity effect. Their dc transport properties, such as the critical and retrapping currents, could be well understood in the diffusive regime. Furthermore, this work lead to the estimation of important parameters in ultra-doped superconducting Si, such as the Fermi velocity, the coherence length, or the electron-phonon coupling constant, fundamental to conceive an all-silicon superconducting electronics.

Bi-2212/1T-TaS2 Van der Waals junctions: Interplay of proximity induced high-Tc superconductivity and CDW order

Understanding the coexistence, competition and/or cooperation between superconductivity and charge density waves (CDWs) in the transition metal dichalcogenides (TMDs) is an elusive goal which, when realized, promises to reveal fundamental information on this important class of materials. Here, we use four-terminal current-voltage measurements to study the Van der Waals interface between freshly exfoliated flakes of the high-Tc superconductor, Bi-2212, and the CDW-dominated TMD layered material, 1T-TaS2. For highly transparent barriers, there is a pronounced Andreev reflection feature providing evidence for proximity-induced high-Tc superconductivity in 1T-TaS2 with a surprisingly large energy gap (~20 meV) equal to half that of intrinsic Bi-2212 (~40 meV). Our systematic study using conductance spectroscopy of junctions with different transparencies also reveals the presence of two separate boson modes, each associated with a “dip-hump” structure. We infer that the proximity-induced high-Tc superconductivity in the 1T-TaS2 is driven by coupling to the metastable metallic phase coexisting within the Mott commensurate CDW (CCDW) phase and associated with a concomitant change of the CCDW order parameter in the interfacial region.

Proximity-Induced Superconductivity in New Superstructures on 2H-NbSe Surface**Supported by the National Natural Science Foundation of China under Grant Nos 11574372 and 11322432, and the ‘Strategic Priority Research Program (B)’ of the Chinese Academy of Sciences under Grant No XDB07020300.

Using scanning tunneling microscopy we observe a stripe phase smoothly interfacing with a triangular 2 × 2 superstructure on the surface of 2H-NbSe single crystal. Proximity-induced superconductivity is demonstrated in these new ordered structures by measurements of low-temperature tunneling spectra. The modulation of superconductivity by the reconstruction provides an opportunity to understand the interplay between superconductivity and charge orders.

Tunable magnetic textures: From Majorana bound states to braiding

A versatile control of magnetic systems, widely used to store information, can also enable manipulating Majorana bounds states (MBS) and implementing fault-tolerant quantum information processing. The proposed platform relies on the proximity-induced superconductivity in a two-dimensional electron gas placed next to an array of magnetic tunnel junctions (MTJs). A change in the magnetization configuration in the MTJ array creates tunable magnetic textures thereby removing several typical requirements for MBS: strong spin-orbit coupling, applied magnetic field, and confinement by one-dimensional structures which complicates demonstrating non-Abelian statistics through braiding. Recent advances in fabricating two-dimensional epitaxial superconductor/semiconductor heterostructures and designing tunable magnetic textures support the feasibility of this novel platform for MBS.