Hard gap in epitaxial semiconductor-superconductor nanowires

Spin-Orbit Protection of Induced Superconductivity in Majorana Nanowires

Spin-orbit interaction (SOI) plays a key role in creating Majorana zero modes in semiconductor nanowires proximity coupled to a superconductor. We track the evolution of the induced superconducting gap in InSb nanowires coupled to a NbTiN superconductor in a large range of magnetic field strengths and orientations. Based on realistic simulations of our devices, we reveal SOI with a strength of 0.15-0.35 eV Å. Our approach identifies the direction of the spin-orbit field, which is strongly affected by the superconductor geometry and electrostatic gates.

Electrostatic formation of the Majorana quasiparticles in the quantum dot-nanoring structure

Zero-energy Majorana quasiparticles can be induced at the edges of low dimensional systems. Non-Abelian statistics of these states make them valid candidates for the realisation of topological quantum computer. From the practical point of view, it is crucial to obtain a system in which an on demand creation and manipulation of this type of bound states is feasible. In this article, we show such a possibility in a setup comprising a quantum nanoring in which we specify a quantum dot region via electrostatic means. The presence of quantum dot can lead to the emergence of Andreev and Majorana bound states in the investigated system. We study the differences between those two types of bound states and the possibility of their manipulation. Moreover, the exact calculation method for spectral function has been proposed, which can be used to study the influence of bound states on the band structure of the proposed system. Using this method, it can be shown that the Majorana bound states, induced at the edge of the system, present themselves as a dispersionless zero-energy flat-band.

Concomitant opening of a bulk-gap with an emerging possible Majorana zero mode

Majorana quasiparticles are generally detected in a 1D topological superconductor by tunneling electrons into its edge, with an emergent zero-bias conductance peak (ZBCP). However, such a ZBCP can also result from other mechanisms, hence, additional verifications are required. Since the emergence of a Majorana must be accompanied by an opening of a topological gap in the bulk, two simultaneous measurements are performed: one in the bulk and another at the edge of a 1D InAs nanowire coated with epitaxial aluminum. Only under certain experimental parameters, a closing of the superconducting bulk-gap that is followed by its reopening, appears simultaneously with a ZBCP at the edge. Such events suggest the occurrence of a topologically non-trivial phase. Yet, we also find that ZBCPs are observed under different tuning parameters without simultaneous reopening of a bulk-gap. This demonstrates the importance of simultaneous probing of bulk and edge in the identification of Majorana edge-states.

Second-Order Topological Superconductivity in π-Junction Rashba Layers

We consider a Josephson junction bilayer consisting of two tunnel-coupled two-dimensional electron gas layers with Rashba spin-orbit interaction, proximitized by a top and bottom s-wave superconductor with phase difference ϕ close to π. We show that, in the presence of a finite weak in-plane Zeeman field, the bilayer can be driven into a second order topological superconducting phase, hosting two Majorana corner states (MCSs). If ϕ=π, in a rectangular geometry, these zero-energy bound states are located at two opposite corners determined by the direction of the Zeeman field. If the phase difference ϕ deviates from π by a critical value, one of the two MCSs gets relocated to an adjacent corner. As the phase difference ϕ increases further, the system becomes trivially gapped. The obtained MCSs are robust against static and magnetic disorder. We propose two setups that could realize such a model: one is based on controlling ϕ by magnetic flux, the other involves an additional layer of randomly oriented magnetic impurities responsible for the phase shift of π in the proximity-induced superconducting pairing.

Germanium Quantum-Well Josephson Field-Effect Transistors and Interferometers

Hybrid superconductor-semiconductor structures attract increasing attention owing to a variety of potential applications in quantum computing devices. They can serve the realization of topological superconducting systems as well as gate-tunable superconducting quantum bits. Here, we combine a SiGe/Ge/SiGe quantum-well heterostructure hosting high-mobility two-dimensional holes and aluminum superconducting leads to realize prototypical hybrid devices, such as Josephson field-effect transistors (JoFETs) and superconducting quantum interference devices (SQUIDs). We observe gate-controlled supercurrent transport with Ge channels as long as one micrometer and estimate the induced superconducting gap from tunnel spectroscopy measurements. Transmission electron microscopy reveals the diffusion of Ge into the Al contacts, whereas no Al is detected in the Ge channel.

Nontopological Majorana Zero Modes in Inhomogeneous Spin Ladders

We show that the coupling of homogeneous Heisenberg spin-1/2 ladders in different phases leads to the formation of interfacial zero energy Majorana bound states. Unlike Majorana bound states at the interfaces of topological quantum wires, these states are void of topological protection and generally susceptible to local perturbations of the host spin system. However, a key message of our Letter is that, in practice, they show a high degree of resilience over wide parameter ranges which may make them interesting candidates for applications.

High-Temperature Majorana Corner States

Majorana bound states often occur at the end of a 1D topological superconductor. Validated by a new bulk invariant and an intuitive edge argument, we show the emergence of one Majorana Kramers pair at each corner of a square-shaped 2D topological insulator proximitized by an s_{±}-wave (e.g., Fe-based) superconductor. We obtain a phase diagram that addresses the relaxation of crystal symmetry and edge orientation. We propose two experimental realizations in candidate materials. Our scheme offers a higher-order and higher-temperature route for exploring non-Abelian quasiparticles.

Spin-Orbit Interaction and Induced Superconductivity in a One-Dimensional Hole Gas

Low dimensional semiconducting structures with strong spin-orbit interaction (SOI) and induced superconductivity attracted great interest in the search for topological superconductors. Both the strong SOI and hard superconducting gap are directly related to the topological protection of the predicted Majorana bound states. Here we explore the one-dimensional hole gas in germanium silicon (Ge-Si) core-shell nanowires (NWs) as a new material candidate for creating a topological superconductor. Fitting multiple Andreev reflection measurements shows that the NW has two transport channels only, underlining its one-dimensionality. Furthermore, we find anisotropy of the Landé g-factor that, combined with band structure calculations, provides us qualitative evidence for the direct Rashba SOI and a strong orbital effect of the magnetic field. Finally, a hard superconducting gap is found in the tunneling regime and the open regime, where we use the Kondo peak as a new tool to gauge the quality of the superconducting gap.

Selective-Area Superconductor Epitaxy to Ballistic Semiconductor Nanowires

Semiconductor nanowires such as InAs and InSb are promising materials for studying Majorana zero modes and demonstrating non-Abelian particle exchange relevant for topological quantum computing. While evidence for Majorana bound states in nanowires has been shown, the majority of these experiments are marked by significant disorder. In particular, the interfacial inhomogeneity between the superconductor and nanowire is strongly believed to be the main culprit for disorder and the resulting "soft superconducting gap" ubiquitous in tunneling studies of hybrid semiconductor-superconductor systems. Additionally, a lack of ballistic transport in nanowire systems can create bound states that mimic Majorana signatures. We resolve these problems through the development of selective-area epitaxy of Al to InSb nanowires, a technique applicable to other nanowires and superconductors. Epitaxial InSb-Al devices generically possess a hard superconducting gap and demonstrate ballistic 1D superconductivity and near-perfect transmission of supercurrents in the single mode regime, requisites for engineering and controlling 1D topological superconductivity. Additionally, we demonstrate that epitaxial InSb-Al superconducting island devices, the building blocks for Majorana-based quantum computing applications, prepared using selective-area epitaxy can achieve micron-scale ballistic 1D transport. Our results pave the way for the development of networks of ballistic superconducting electronics for quantum device applications.

Selective-Area-Grown Semiconductor-Superconductor Hybrids: A Basis for Topological Networks

We introduce selective area grown hybrid InAs/Al nanowires based on molecular beam epitaxy, allowing arbitrary semiconductor-superconductor networks containing loops and branches. Transport reveals a hard induced gap and unpoisoned 2e-periodic Coulomb blockade, with temperature dependent 1e features in agreement with theory. Coulomb peak spacing in parallel magnetic field displays overshoot, indicating an oscillating discrete near-zero subgap state consistent with device length. Finally, we investigate a loop network, finding strong spin-orbit coupling and a coherence length of several microns. These results demonstrate the potential of this platform for scalable topological networks among other applications.

A ballistic graphene superconducting microwave circuit

Josephson junctions (JJ) are a fundamental component of microwave quantum circuits, such as tunable cavities, qubits, and parametric amplifiers. Recently developed encapsulated graphene JJs, with supercurrents extending over micron distance scales, have exciting potential applications as a new building block for quantum circuits. Despite this, the microwave performance of this technology has not been explored. Here, we demonstrate a microwave circuit based on a ballistic graphene JJ embedded in a superconducting cavity. We directly observe a gate-tunable Josephson inductance through the resonance frequency of the device and, using a detailed RF model, we extract this inductance quantitatively. We also observe the microwave losses of the device, and translate this into sub-gap resistances of the junction at μeV energy scales, not accessible in DC measurements. The microwave performance we observe here suggests that graphene Josephson junctions are a feasible platform for implementing coherent quantum circuits.

Metal oxide modified ZnO nanomaterials for biosensor applications

Advancing as a biosensing nanotechnology, nanohybrids present a new class of functional materials with high selectivity and sensitivity, enabling integration of nanoscale chemical/biological interactions with biomedical devices. The unique properties of ZnO combined with metal oxide nanostructures were recently demonstrated to be an efficient approach for sensor device fabrication with accurate, real-time and high-throughput biosensing, creating new avenues for diagnosis, disease management and therapeutics. This review article collates recent advances in the modified ZnO nanostructured metal oxide nanohybrids for efficient enzymatic and non-enzymatic biosensor applications. Furthermore, we also discussed future prospects for nanohybrid materials to yield high-performance biosensor devices.

Quantum engineering of Majorana quasiparticles in one-dimensional optical lattices

We propose a feasible way of engineering Majorana-type quasiparticles in ultracold fermionic gases on a one-dimensional (1D) optical lattice. For this purpose, imbalanced ultracold atoms interacting by the spin-orbit coupling should be hybridized with a three-dimensional Bose-Einstein condensate molecular cloud. We show that the Majorana-type excitations can be created or annihilated upon constraining the profile of a trapping potential and/or an internal scattering barier. This process is modeled within the Bogoliubov-de Gennes approach. Our study is relevant also to nanoscopic 1D superconductors, where both potentials can be imposed by electrostatic means.

Direct Microwave Measurement of Andreev-Bound-State Dynamics in a Semiconductor-Nanowire Josephson Junction

The modern understanding of the Josephson effect in mesosopic devices derives from the physics of Andreev bound states, fermionic modes that are localized in a superconducting weak link. Recently, Josephson junctions constructed using semiconducting nanowires have led to the realization of superconducting qubits with gate-tunable Josephson energies. We have used a microwave circuit QED architecture to detect Andreev bound states in such a gate-tunable junction based on an aluminum-proximitized indium arsenide nanowire. We demonstrate coherent manipulation of these bound states, and track the bound-state fermion parity in real time. Individual parity-switching events due to nonequilibrium quasiparticles are observed with a characteristic timescale T_{parity}=160±10  μs. The T_{parity} of a topological nanowire junction sets a lower bound on the bandwidth required for control of Majorana bound states.

Perfect Strain Relaxation in Metamorphic Epitaxial Aluminum on Silicon through Primary and Secondary Interface Misfit Dislocation Arrays

Understanding the atomically precise arrangement of atoms at epitaxial interfaces is important for emerging technologies such as quantum materials that have function and performance dictated by bonds and defects that are energetically active on the micro-electronvolt scale. A combination of atomistic modeling and dislocation theory analysis describes both primary and secondary dislocation networks at the metamorphic Al/Si (111) interface, which is experimentally validated by atomic resolution scanning transmission electron microscopy. The electron microscopy images show primary misfit dislocations for the majority of the strain relief and evidence of a secondary structure allowing for complete relaxation of the Al-Si misfit strain. This study demonstrates the equilibrium interface that represents the lowest energy structure of a highly mismatched and semicoherent single-crystal interface with complete strain relief in an atomically abrupt structure.

Effective g Factor of Subgap States in Hybrid Nanowires

We use the effective g factor of Andreev subgap states in an axial magnetic field to investigate how the superconducting density of states is distributed between the semiconductor core and the superconducting shell in hybrid nanowires. We find a steplike reduction of the Andreev g factor and an improved hard gap with reduced carrier density in the nanowire, controlled by gate voltage. These observations are relevant for Majorana devices, which require tunable carrier density and a g factor exceeding that of the parent superconductor.

Andreev spectrum and supercurrents in nanowire-based SNS junctions containing Majorana bound states

Hybrid superconductor-semiconductor nanowires with Rashba spin-orbit coupling are arguably becoming the leading platform for the search of Majorana bound states (MBSs) in engineered topological superconductors. We perform a systematic numerical study of the low-energy Andreev spectrum and supercurrents in short and long superconductor-normal-superconductor junctions made of nanowires with strong Rashba spin-orbit coupling, where an external Zeeman field is applied perpendicular to the spin-orbit axis. In particular, we investigate the detailed evolution of the Andreev bound states from the trivial into the topological phase and their relation with the emergence of MBSs. Due to the finite length, the system hosts four MBSs, two at the inner part of the junction and two at the outer one. They hybridize and give rise to a finite energy splitting at a superconducting phase difference of π, a well-visible effect that can be traced back to the evolution of the energy spectrum with the Zeeman field: from the trivial phase with Andreev bound states into the topological phase with MBSs. Similarly, we carry out a detailed study of supercurrents for short and long junctions from the trivial to the topological phases. The supercurrent, calculated from the Andreev spectrum, is 2π-periodic in the trivial and topological phases. In the latter it exhibits a clear sawtooth profile at a phase difference of π when the energy splitting is negligible, signalling a strong dependence of current-phase curves on the length of the superconducting regions. Effects of temperature, scalar disorder and reduction of normal transmission on supercurrents are also discussed. Further, we identify the individual contribution of MBSs. In short junctions the MBSs determine the current-phase curves, while in long junctions the spectrum above the gap (quasi-continuum) introduces an important contribution.

Proximity effect in a two-dimensional electron gas coupled to a thin superconducting layer

There have recently been several experiments studying induced superconductivity in semiconducting two-dimensional electron gases that are strongly coupled to thin superconducting layers, as well as probing possible topological phases supporting Majorana bound states in such setups. We show that a large band shift is induced in the semiconductor by the superconductor in this geometry, thus making it challenging to realize a topological phase. Additionally, we show that while increasing the thickness of the superconducting layer reduces the magnitude of the band shift, it also leads to a more significant renormalization of the semiconducting material parameters and does not reduce the challenge of tuning into a topological phase.

Inverse proximity effect in semiconductor Majorana nanowires

We study the influence of the inverse proximity effect on the superconductivity nucleation in hybrid structures consisting of semiconducting nanowires placed in contact with a thin superconducting film and discuss the resulting restrictions on the operation of Majorana-based devices. A strong paramagnetic effect for electrons entering the semiconductor together with spin-orbit coupling and van Hove singularities in the electronic density of states in the wire are responsible for the suppression of superconducting correlations in the low-field domain and for the reentrant superconductivity at high magnetic fields in the topologically nontrivial regime. The growth of the critical temperature in the latter case continues up to the upper critical field destroying the pairing inside the superconducting film due to either orbital or paramagnetic mechanism. The suppression of the homogeneous superconducting state near the boundary between the topological and non-topological regimes provides the conditions favorable for the Fulde-Ferrel-Larkin-Ovchinnikov instability.

Evolution of Nanowire Transmon Qubits and Their Coherence in a Magnetic Field

We present an experimental study of flux- and gate-tunable nanowire transmons with state-of-the-art relaxation time allowing quantitative extraction of flux and charge noise coupling to the Josephson energy. We evidence coherence sweet spots for charge, tuned by voltage on a proximal side gate, where first order sensitivity to switching two-level systems and background 1/f noise is minimized. Next, we investigate the evolution of a nanowire transmon in a parallel magnetic field up to 70 mT, the upper bound set by the closing of the induced gap. Several features observed in the field dependence of qubit energy relaxation and dephasing times are not fully understood. Using nanowires with a thinner, partially covering Al shell will enable operation of these circuits up to 0.5 T, a regime relevant for topological quantum computation and other applications.

Ballistic Majorana nanowire devices

Majorana modes are zero-energy excitations of a topological superconductor that exhibit non-Abelian statistics1-3. Following proposals for their detection in a semiconductor nanowire coupled to an s-wave superconductor4,5, several tunnelling experiments reported characteristic Majorana signatures6-11. Reducing disorder has been a prime challenge for these experiments because disorder can mimic the zero-energy signatures of Majoranas12-16, and renders the topological properties inaccessible17-20. Here, we show characteristic Majorana signatures in InSb nanowire devices exhibiting clear ballistic transport properties. Application of a magnetic field and spatial control of carrier density using local gates generates a zero bias peak that is rigid over a large region in the parameter space of chemical potential, Zeeman energy and tunnel barrier potential. The reduction of disorder allows us to resolve separate regions in the parameter space with and without a zero bias peak, indicating topologically distinct phases. These observations are consistent with the Majorana theory in a ballistic system 21 , and exclude the known alternative explanations that invoke disorder12-16 or a nonuniform chemical potential22,23.

Robust Epitaxial Al Coating of Reclined InAs Nanowires

It was recently shown that in situ epitaxial aluminum coating of indium arsenide nanowires is possible and yields superior properties relative to ex-situ evaporation of aluminum ( Nat. Mater. 2015 , 14 , 400 - 406 ). We demonstrate a robust and adaptive epitaxial growth protocol satisfying the need for producing an intimate contact between the aluminum superconductor and the indium arsenide nanowire. We show that the (001) indium arsenide substrate allows successful aluminum side-coating of reclined indium arsenide nanowires that emerge from (111)B microfacets. A robust, induced hard superconducting gap in the obtained indium arsenide/aluminum core/partial shell nanowires is clearly demonstrated. We compare epitaxial side-coating of round and hexagonal cross-section nanowires and find the surface roughness of the round nanowires to induce a more uniform aluminum profile. Consequently, the extended aluminum grains result in increased strain at the interface with the indium arsenide nanowire, which is found to induce dislocations penetrating into round nanowires only. A unique feature of proposed growth protocol is that it supports in situ epitaxial deposition of aluminum on all three arms of indium arsenide nanowire intersections in a single growth step. Such aluminum coated intersections play a key role in engineering topologically superconducting networks required for Majorana based quantum computation schemes.

Influence of the orbital effects on the Majorana quasi-particles in a nanowire

Majorana quasi-particles can be realised using magnetic field in the form of diamagnetic (orbital) or paramagnetic effects. In both cases, the magnetic field induces a topologically non-trivial phase of matter. In this paper, the influence of orbital effects on Majorana bound states induced by paramagnetic effects in 1D nanowire is elaborated. The role of orbital effects in density of states and eigenstates of the system is also discussed. Additionally, we show the phase diagram-the magnetic field versus the magnetic flux, which displays a relation between topologically trivial and non-trivial phases. The Majorana bound states existence in the presence of relatively small orbital effects is indicated.

Zero-Energy Modes from Coalescing Andreev States in a Two-Dimensional Semiconductor-Superconductor Hybrid Platform

We investigate zero-bias conductance peaks that arise from coalescing subgap Andreev states, consistent with emerging Majorana zero modes, in hybrid semiconductor-superconductor wires defined in a two-dimensional InAs/Al heterostructure using top-down lithography and gating. The measurements indicate a hard superconducting gap, ballistic tunneling contact, and in-plane critical fields up to 3 T. Top-down lithography allows complex geometries, branched structures, and straightforward scaling to multicomponent devices compared to structures made from assembled nanowires.

Scaling of Majorana Zero-Bias Conductance Peaks

We report an experimental study of the scaling of zero-bias conductance peaks compatible with Majorana zero modes as a function of magnetic field, tunnel coupling, and temperature in one-dimensional structures fabricated from an epitaxial semiconductor-superconductor heterostructure. Results are consistent with theory, including a peak conductance that is proportional to tunnel coupling, saturates at 2e^{2}/h, decreases as expected with field-dependent gap, and collapses onto a simple scaling function in the dimensionless ratio of temperature and tunnel coupling.

Andreev molecules in semiconductor nanowire double quantum dots

Chains of quantum dots coupled to superconductors are promising for the realization of the Kitaev model of a topological superconductor. While individual superconducting quantum dots have been explored, control of longer chains requires understanding of interdot coupling. Here, double quantum dots are defined by gate voltages in indium antimonide nanowires. High transparency superconducting niobium titanium nitride contacts are made to each of the dots in order to induce superconductivity, as well as probe electron transport. Andreev bound states induced on each of dots hybridize to define Andreev molecular states. The evolution of these states is studied as a function of charge parity on the dots, and in magnetic field. The experiments are found in agreement with a numerical model.

Quantum dots in a nanowire are one possible approach to creating a solid-state quantum simulator. Here, the authors demonstrate the coupling of electronic states in a double quantum dot to form Andreev molecule states; a potential building block for longer chains suitable for quantum simulation.

Quantum Criticality in Resonant Andreev Conduction

Motivated by recent experiments with proximitized nanowires, we study a mesoscopic s-wave superconductor connected via point contacts to normal-state leads. We demonstrate that at energies below the charging energy the system is described by the two-channel Kondo model, which can be brought to the quantum critical regime by varying the gate potential and conductances of the contacts.

Experimental phase diagram of zero-bias conductance peaks in superconductor/semiconductor nanowire devices

Topological superconductivity is an exotic state of matter characterized by spinless p-wave Cooper pairing of electrons and by Majorana zero modes at the edges. The first signature of topological superconductivity is a robust zero-bias peak in tunneling conductance. We perform tunneling experiments on semiconductor nanowires (InSb) coupled to superconductors (NbTiN) and establish the zero-bias peak phase in the space of gate voltage and external magnetic field. Our findings are consistent with calculations for a finite-length topological nanowire and provide means for Majorana manipulation as required for braiding and topological quantum bits.

Orbital Contributions to the Electron g Factor in Semiconductor Nanowires

Recent experiments on Majorana fermions in semiconductor nanowires [S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, and C. M. Marcus, Nature (London) 531, 206 (2016)NATUAS0028-083610.1038/nature17162] revealed a surprisingly large electronic Landé g factor, several times larger than the bulk value-contrary to the expectation that confinement reduces the g factor. Here we assess the role of orbital contributions to the electron g factor in nanowires and quantum dots. We show that an L·S coupling in higher subbands leads to an enhancement of the g factor of an order of magnitude or more for small effective mass semiconductors. We validate our theoretical finding with simulations of InAs and InSb, showing that the effect persists even if cylindrical symmetry is broken. A huge anisotropy of the enhanced g factors under magnetic field rotation allows for a straightforward experimental test of this theory.

Ballistic superconductivity in semiconductor nanowires

Semiconductor nanowires have opened new research avenues in quantum transport owing to their confined geometry and electrostatic tunability. They have offered an exceptional testbed for superconductivity, leading to the realization of hybrid systems combining the macroscopic quantum properties of superconductors with the possibility to control charges down to a single electron. These advances brought semiconductor nanowires to the forefront of efforts to realize topological superconductivity and Majorana modes. A prime challenge to benefit from the topological properties of Majoranas is to reduce the disorder in hybrid nanowire devices. Here we show ballistic superconductivity in InSb semiconductor nanowires. Our structural and chemical analyses demonstrate a high-quality interface between the nanowire and a NbTiN superconductor that enables ballistic transport. This is manifested by a quantized conductance for normal carriers, a strongly enhanced conductance for Andreev-reflecting carriers, and an induced hard gap with a significantly reduced density of states. These results pave the way for disorder-free Majorana devices.

Method for determining optimal supercell representation of interfaces

The geometry and structure of an interface ultimately determines the behavior of devices at the nanoscale. We present a generic method to determine the possible lattice matches between two arbitrary surfaces and to calculate the strain of the corresponding matched interface. We apply this method to explore two relevant classes of interfaces for which accurate structural measurements of the interface are available: (i) the interface between pentacene crystals and the (1 1 1) surface of gold, and (ii) the interface between the semiconductor indium-arsenide and aluminum. For both systems, we demonstrate that the presented method predicts interface geometries in good agreement with those measured experimentally, which present nontrivial matching characteristics and would be difficult to guess without relying on automated structure-searching methods.

Inducing superconductivity in Weyl semimetal microstructures by selective ion sputtering

By introducing a superconducting gap in Weyl or Dirac semimetals, the superconducting state inherits the nontrivial topology of their electronic structure. As a result, Weyl superconductors are expected to host exotic phenomena, such as nonzero-momentum pairing due to their chiral node structure, or zero-energy Majorana modes at the surface. These are of fundamental interest to improve our understanding of correlated topological systems, and, moreover, practical applications in phase-coherent devices and quantum applications have been proposed. Proximity-induced superconductivity promises to allow these experiments on nonsuperconducting Weyl semimetals. We show a new route to reliably fabricate superconducting microstructures from the nonsuperconducting Weyl semimetal NbAs under ion irradiation. The significant difference in the surface binding energy of Nb and As leads to a natural enrichment of Nb at the surface during ion milling, forming a superconducting surface layer (T_c ~ 3.5 K). Being formed from the target crystal itself, the ideal contact between the superconductor and the bulk may enable an effective gapping of the Weyl nodes in the bulk because of the proximity effect. Simple ion irradiation may thus serve as a powerful tool for the fabrication of topological quantum devices from monoarsenides, even on an industrial scale.

Hard Superconducting Gap in InSb Nanowires

Topological superconductivity is a state of matter that can host Majorana modes, the building blocks of a topological quantum computer. Many experimental platforms predicted to show such a topological state rely on proximity-induced superconductivity. However, accessing the topological properties requires an induced hard superconducting gap, which is challenging to achieve for most material systems. We have systematically studied how the interface between an InSb semiconductor nanowire and a NbTiN superconductor affects the induced superconducting properties. Step by step, we improve the homogeneity of the interface while ensuring a barrier-free electrical contact to the superconductor and obtain a hard gap in the InSb nanowire. The magnetic field stability of NbTiN allows the InSb nanowire to maintain a hard gap and a supercurrent in the presence of magnetic fields (∼0.5 T), a requirement for topological superconductivity in one-dimensional systems. Our study provides a guideline to induce superconductivity in various experimental platforms such as semiconductor nanowires, two-dimensional electron gases, and topological insulators and holds relevance for topological superconductivity and quantum computation.

Transport Signatures of Quasiparticle Poisoning in a Majorana Island

We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (∼1  μs) and sets a bound for a weakly coupled island (>10  μs). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. When converted from gate voltage to energy units, fluctuations are consistent with previous measurements.

Direct Cavity Detection of Majorana Pairs

No experiment could directly test the particle-antiparticle duality of Majorana fermions, so far. However, this property represents a necessary ingredient towards the realization of topological quantum computing schemes. Here, we show how to complete this task by using microwave techniques. The direct coupling between a pair of overlapping Majorana bound states and the electric field from a microwave cavity is extremely difficult to detect due to the self-adjoint character of Majorana fermions which forbids direct energy exchanges with the cavity. We show theoretically how this problem can be circumvented by using photoassisted tunneling to fermionic reservoirs. The absence of a direct microwave transition inside the Majorana pair in spite of the light-Majorana coupling would represent a smoking gun for the Majorana self-adjoint character.

Proximity-Induced Shiba States in a Molecular Junction

Superconductors containing magnetic impurities exhibit intriguing phenomena derived from the competition between Cooper pairing and Kondo screening. At the heart of this competition are the Yu-Shiba-Rusinov (Shiba) states which arise from the pair breaking effects a magnetic impurity has on a superconducting host. Hybrid superconductor-molecular junctions offer unique access to these states but the added complexity in fabricating such devices has kept their exploration to a minimum. Here, we report on the successful integration of a model spin 1/2 impurity, in the form of a neutral and stable all organic radical molecule, in proximity-induced superconducting break junctions. Our measurements reveal excitations which are characteristic of a spin-induced Shiba state due to the radical's unpaired spin strongly coupled to a superconductor. By virtue of a variable molecule-electrode coupling, we access both the singlet and doublet ground states of the hybrid system which give rise to the doublet and singlet Shiba excited states, respectively. Our results show that Shiba states are a robust feature of the interaction between a paramagnetic impurity and a proximity-induced superconductor where the excited state is mediated by correlated electron-hole (Andreev) pairs instead of Cooper pairs.

Normal, superconducting and topological regimes of hybrid double quantum dots

Epitaxial semiconductor-superconductor hybrid materials are an excellent basis for studying mesoscopic and topological superconductivity, as the semiconductor inherits a hard superconducting gap while retaining tunable carrier density. Here, we investigate double-quantum-dot structures made from InAs nanowires with a patterned epitaxial Al two-facet shell that proximitizes two gate-defined segments along the nanowire. We follow the evolution of mesoscopic superconductivity and charging energy in this system as a function of magnetic field and voltage-tuned barriers. Interdot coupling is varied from strong to weak using side gates, and the ground state is varied between normal, superconducting and topological regimes by applying a magnetic field. We identify the topological transition by tracking the spacing between successive co-tunnelling peaks as a function of axial magnetic field and show that the individual dots host weakly hybridized Majorana modes.

Nb/InAs nanowire proximity junctions from Josephson to quantum dot regimes

The superconducting proximity effect is probed experimentally in Josephson junctions fabricated with InAs nanowires contacted by Nb leads. Contact transparencies [Formula: see text] are observed. The electronic phase coherence length at low temperatures exceeds the channel length. However, the elastic scattering length is a few times shorter than the channel length. Electrical measurements reveal two regimes of quantum transport: (i) the Josephson regime, characterised by a dissipationless current up to ∼100 nA, and (ii) the quantum dot (QD) regime, characterised by the formation of Andreev bound states (ABS) associated with spontaneous QDs inside the nanowire channel. In regime (i), the behaviour of the critical current I _c versus an axial magnetic field [Formula: see text] shows an unexpected modulation and persistence to fields [Formula: see text] T. In the QD regime, the ABS are modelled as the current-biased solutions of an Anderson-type model. The applicability of devices in both transport regimes to Majorana fermion experiments is discussed.

Controlled growth of hexagonal gold nanostructures during thermally induced self-assembling on Ge(001) surface

Nano-sized gold has become an important material in various fields of science and technology, where control over the size and crystallography is desired to tailor the functionality. Gold crystallizes in the face-centered cubic (fcc) phase, and its hexagonal closed packed (hcp) structure is a very unusual and rare phase. Stable Au hcp phase has been reported to form in nanoparticles at the tips of some Ge nanowires. It has also recently been synthesized in the form of thin graphene-supported sheets which are unstable under electron beam irradiation. Here, we show that stable hcp Au 3D nanostructures with well-defined crystallographic orientation and size can be systematically created in a process of thermally induced self-assembly of thin Au layer on Ge(001) monocrystal. The Au hcp crystallite is present in each Au nanostructure and has been characterized by different electron microscopy techniques. We report that a careful heat treatment above the eutectic melting temperature and a controlled cooling is required to form the hcp phase of Au on a Ge single crystal. This new method gives scientific prospects to obtain stable Au hcp phase for future applications in a rather simple manner as well as redefine the phase diagram of Gold with Germanium.

Proximity Effect Transfer from NbTi into a Semiconductor Heterostructure via Epitaxial Aluminum

We demonstrate the transfer of the superconducting properties of NbTi, a large-gap high-critical-field superconductor, into an InAs heterostructure via a thin intermediate layer of epitaxial Al. Two device geometries, a Josephson junction and a gate-defined quantum point contact, are used to characterize interface transparency and the two-step proximity effect. In the Josephson junction, multiple Andreev reflections reveal near-unity transparency with an induced gap Δ* = 0.50 meV and a critical temperature of 7.8 K. Tunneling spectroscopy yields a hard induced gap in the InAs adjacent to the superconductor of Δ* = 0.43 meV with substructure characteristic of both Al and NbTi.

Noncollinear Spin-Orbit Magnetic Fields in a Carbon Nanotube Double Quantum Dot

We demonstrate experimentally that noncollinear intrinsic spin-orbit magnetic fields can be realized in a curved carbon nanotube two-segment device. Each segment, analyzed in the quantum dot regime, shows near fourfold degenerate shell structure allowing for identification of the spin-orbit coupling and the angle between the two segments. Furthermore, we determine the four unique spin directions of the quantum states for specific shells and magnetic fields. This class of quantum dot systems is particularly interesting when combined with induced superconducting correlations as it may facilitate unconventional superconductivity and detection of Cooper pair entanglement. Our device comprises the necessary elements.

Quantized conductance doubling and hard gap in a two-dimensional semiconductor-superconductor heterostructure

Coupling a two-dimensional (2D) semiconductor heterostructure to a superconductor opens new research and technology opportunities, including fundamental problems in mesoscopic superconductivity, scalable superconducting electronics, and new topological states of matter. One route towards topological matter is by coupling a 2D electron gas with strong spin–orbit interaction to an s-wave superconductor. Previous efforts along these lines have been adversely affected by interface disorder and unstable gating. Here we show measurements on a gateable InGaAs/InAs 2DEG with patterned epitaxial Al, yielding devices with atomically pristine interfaces between semiconductor and superconductor. Using surface gates to form a quantum point contact (QPC), we find a hard superconducting gap in the tunnelling regime. When the QPC is in the open regime, we observe a first conductance plateau at 4e²/h, consistent with theory. The hard-gap semiconductor–superconductor system demonstrated here is amenable to top-down processing and provides a new avenue towards low-dissipation electronics and topological quantum systems.

Interface transparency between 2D semiconductors and superconductors is a longstanding problem, seriously hindering potential applications. Here, using a new hybrid system, Kjaergaard et al. report quantized conductance doubling and a hard superconducting gap measured via a quantum point contact, indicating a near pristine interface.

Spin-Orbit Coupling at the Level of a Single Electron

We utilize electron counting techniques to distinguish a spin-conserving fast tunneling process and a slower process involving spin flips in AlGaAs/GaAs-based double quantum dots. By studying the dependence of the rates on the interdot tunnel coupling of the two dots, we find that as many as 4% of the tunneling events occur with a spin flip related to spin-orbit coupling in GaAs. Our measurement has a fidelity of 99% in terms of resolving whether a tunneling event occurred with a spin flip or not.

Semiconductor-inspired design principles for superconducting quantum computing

Superconducting circuits offer tremendous design flexibility in the quantum regime culminating most recently in the demonstration of few qubit systems supposedly approaching the threshold for fault-tolerant quantum information processing. Competition in the solid-state comes from semiconductor qubits, where nature has bestowed some very useful properties which can be utilized for spin qubit-based quantum computing. Here we begin to explore how selective design principles deduced from spin-based systems could be used to advance superconducting qubit science. We take an initial step along this path proposing an encoded qubit approach realizable with state-of-the-art tunable Josephson junction qubits. Our results show that this design philosophy holds promise, enables microwave-free control, and offers a pathway to future qubit designs with new capabilities such as with higher fidelity or, perhaps, operation at higher temperature. The approach is also especially suited to qubits on the basis of variable super-semi junctions.

Superconducting circuits offer great promise for quantum computing, but implementations require careful shielding from control electronics. Here, the authors take inspirations from semiconductor spin-based qubits to design Josephson junctions quantum circuits whose qubits do not require microwave control.

Majorana bound states from exceptional points in non-topological superconductors

Recent experimental efforts towards the detection of Majorana bound states have focused on creating the conditions for topological superconductivity. Here we demonstrate an alternative route, which achieves fully localised zero-energy Majorana bound states when a topologically trivial superconductor is strongly coupled to a helical normal region. Such a junction can be experimentally realised by e.g. proximitizing a finite section of a nanowire with spin-orbit coupling, and combining electrostatic depletion and a Zeeman field to drive the non-proximitized (normal) portion into a helical phase. Majorana zero modes emerge in such an open system without fine-tuning as a result of charge-conjugation symmetry, and can be ultimately linked to the existence of ‘exceptional points’ (EPs) in parameter space, where two quasibound Andreev levels bifurcate into two quasibound Majorana zero modes. After the EP, one of the latter becomes non-decaying as the junction approaches perfect Andreev reflection, thus resulting in a Majorana dark state (MDS) localised at the NS junction. We show that MDSs exhibit the full range of properties associated to conventional closed-system Majorana bound states (zero-energy, self-conjugation, 4π-Josephson effect and non-Abelian braiding statistics), while not requiring topological superconductivity.

Towards Realistic Implementations of a Majorana Surface Code

Surface codes have emerged as promising candidates for quantum information processing. Building on the previous idea to realize the physical qubits of such systems in terms of Majorana bound states supported by topological semiconductor nanowires, we show that the basic code operations, namely projective stabilizer measurements and qubit manipulations, can be implemented by conventional tunnel conductance probes and charge pumping via single-electron transistors, respectively. The simplicity of the access scheme suggests that a functional code might be in close experimental reach.

Approaching the Hole Mobility Limit of GaSb Nanowires

In recent years, high-mobility GaSb nanowires have received tremendous attention for high-performance p-type transistors; however, due to the difficulty in achieving thin and uniform nanowires (NWs), there is limited report until now addressing their diameter-dependent properties and their hole mobility limit in this important one-dimensional material system, where all these are essential information for the deployment of GaSb NWs in various applications. Here, by employing the newly developed surfactant-assisted chemical vapor deposition, high-quality and uniform GaSb NWs with controllable diameters, spanning from 16 to 70 nm, are successfully prepared, enabling the direct assessment of their growth orientation and hole mobility as a function of diameter while elucidating the role of sulfur surfactant and the interplay between surface and interface energies of NWs on their electrical properties. The sulfur passivation is found to efficiently stabilize the high-energy NW sidewalls of (111) and (311) in order to yield the thin NWs (i.e., <40 nm in diameters) with the dominant growth orientations of ⟨211⟩ and ⟨110⟩, whereas the thick NWs (i.e., >40 nm in diameters) would grow along the most energy-favorable close-packed planes with the orientation of ⟨111⟩, supported by the approximate atomic models. Importantly, through the reliable control of sulfur passivation, growth orientation and surface roughness, GaSb NWs with the peak hole mobility of ∼400 cm(2)V s(-1) for the diameter of 48 nm, approaching the theoretical limit under the hole concentration of ∼2.2 × 10(18) cm(-3), can be achieved for the first time. All these indicate their promising potency for utilizations in different technological domains.

Realization of Microwave Quantum Circuits Using Hybrid Superconducting-Semiconducting Nanowire Josephson Elements

We report the realization of quantum microwave circuits using hybrid superconductor-semiconductor Josephson elements comprised of InAs nanowires contacted by NbTiN. Capacitively shunted single elements behave as transmon circuits with electrically tunable transition frequencies. Two-element circuits also exhibit transmonlike behavior near zero applied flux but behave as flux qubits at half the flux quantum, where nonsinusoidal current-phase relations in the elements produce a double-well Josephson potential. These hybrid Josephson elements are promising for applications requiring microwave superconducting circuits operating in a magnetic field.