Semiconductor/superconductor hybrids exhibit a range of phenomena that can be exploited for the study of novel physics and the development of new technologies. Understanding the origin the energy spectrum of such hybrids is therefore a crucial goal. Here, we study Josephson junctions defined by shadow epitaxy on InAsSb/Al nanowires. The devices exhibit gate-tunable supercurrents at low temperatures and multiple Andreev reflections (MARs) at finite voltage bias. Under microwave irradiation, photon assisted tunneling (PAT) of MARs produces characteristic oscillating sidebands at quantized energies, which depend on MAR order, $n$, in agreement with a recently suggested modification of the classical Tien-Gordon equation. The scaling of the quantized energy spacings with microwave frequency provides independent confirmation of the effective charge $ne$ transferred by the $n^\mathrm{th}$ order tunnel process. The measurements suggest PAT as a powerful method for assigning the origin of low energy spectral features in hybrid Josephson devices.
We theoretically analyze the Andreev bound states and their coupling to external radiation in superconductor-nanowire-superconductor Josephson junctions. We provide an effective Hamiltonian for the junction projected onto the Andreev level subspace and incorporating the effects of nanowire multichannel structure, Rashba spin-orbit coupling, and Zeeman field. Based on this effective model, we investigate the dependence of the Andreev levels and the matrix elements of the current operator on system parameters such as chemical potential, nanowire dimensions, and normal transmission. We show that …
The charge character of Andreev bound states (ABSs) in a three-terminal semiconductor-superconductor hybrid nanowire was measured using local and nonlocal tunneling spectroscopy. The device is fabricated using an epitaxial InAs/Al two-dimensional heterostructure with several gate-defined side probes. ABSs are found to oscillate around zero as a function of gate voltage, with modifications of their charge consistent with theoretical expectations for the total Bardeen-Cooper- Schrieffer (BCS) charge of ABSs.
We performed microwave spectroscopy of an InAs nanowire between superconducting contacts implementing a finite-length, multi-channel Josephson weak link. Certain features in the spectra, such as the splitting by spin-orbit interactions of the transition lines among Andreev states, have been already understood in terms of non-interacting models. However, we identify here additional transitions, which evidence the presence of Coulomb interactions. By combining experimental measurements and model calculations, we reach a qualitative understanding of these very rich Andreev spectra.
Josephson junctions based on semiconductor nanowires are potential building blocks for electrically tunable qubit structures, e.g. the gatemon or the Andreev qubit. However, an actual realization requires the thorough investigation of the intrinsic excitation spectrum. Here, we demonstrate the fabrication of low-loss superconducting microwave circuits that combine high quality factors with a well-controlled gate architecture by utilizing a flip-chip approach. This platform is then used to perform single-tone and two-tone experiments on Andreev states in in-situ grown InAs/Al core/half-shell na…
Semiconductor nanowires provide promising low-dimensional systems for the study of quantum transport phenomena in combination with superconductivity. Here we investigate the competition between the Coulomb blockade effect, Andreev reflection, and quantum interference, in InAs and InP nanowires connected to aluminum-based superconducting electrodes. We compare three limiting cases depending on the tunnel coupling strength and the characteristic Coulomb interaction energy. For weak coupling and large charging energy, negative differential conductance is observed as a direct consequence of the BC…
We investigate transmon qubits made from semiconductor nanowires with a fully surrounding superconducting shell. In the regime of reentrant superconductivity associated with the destructive Little-Parks effect, numerous coherent transitions are observed in the first reentrant lobe, where the shell carries 2π winding of superconducting phase, and are absent in the zeroth lobe. As junction density was increased by gate voltage, qubit coherence was suppressed then lost in the first lobe. These observations and numerical simulations highlight the role of winding-induced Andreev states in the junct…
We numerically study crossed Andreev reflection (CAR) in a topological insulator nanowire T-junction where one lead is proximitized by a superconductor. We perform realistic simulations based on the 3D BHZ model and compare the results with those from an effective 2D surface model, whose computational cost is much lower. Both approaches show that CAR should be clearly observable in a wide parameter range, including perfect CAR in a somewhat more restricted range. Furthermore, it can be controlled by a magnetic field and is robust to disorder. Our effective 2D implementation allows to model sys…
We study the energy spectrum and the electromagnetic response of Andreev bound states in short Josephson junctions made of semiconducting nanowires. We focus on the joint effect of Zeeman and spin-orbit coupling on the Andreev level spectra. Our model incorporates the penetration of the magnetic field in the proximitized wires, which substantially modifies the spectra. We pay special attention to the occurrence of fermion parity switches at increasing values of the field and to the magnetic field dependence of the absorption strength of microwave-induced transitions. Our calculations can be us…
We show theoretically that in the generic finite chemical potential situation, the clean superconducting spin-orbit-coupled nanowire has two distinct nontopological regimes as a function of Zeeman splitting (below the topological quantum phase transition): one is characterized by finite-energy in-gap Andreev bound states, while the other has only extended bulk states. The Andreev bound state regime is characterized by strong features in the tunneling spectra creating a "gap closure" signature, but no "gap reopening" signature should be apparent above the topological quantum phase transition, i…
We study an analytical model of a Rashba nanowire that is partially covered by and coupled to a thin superconducting layer, where the uncovered region of the nanowire forms a quantum dot. We find that, even if there is no topological superconducting phase possible, there is a trivial Andreev bound state that becomes pinned exponentially close to zero energy as a function of magnetic field strength when the length of the quantum dot is tuned with respect to its spin-orbit length such that a resonance condition of Fabry-Perot type is satisfied. In this case, we find that the Andreev bound state …
Majorana bound states (MBS) and Andreev bound states (ABS) in realistic Majorana nanowires setups have similar experimental signatures which make them hard to distinguishing one from the other. Here, we characterize the continuous Majorana/Andreev crossover interpolating between fully-separated, partially-separated, and fully-overlapping Majorana modes, in terms of global and local topological invariants, fermion parity, quasiparticle densities, Majorana pseudospin and spin polarizations, density overlaps and transition probabilities between opposite Majorana components. We found that in inhom…
Kitaev chain is a theoretical model of a one-dimensional topological superconductor with Majorana zero modes at the two ends of the chain. With the goal of emulating this model, we build a chain of three quantum dots in a semiconductor nanowire. We observe Andreev bound states in each of the three dots and study their magnetic field and gate voltage dependence. Theory indicates that triple dot states acquire Majorana polarization when Andreev states in all three dots reach zero energy in a narrow range of magnetic field. In our device Andreev states in one of the dots reach zero energy at a lo…
Quantum simulation is a way to study unexplored Hamiltonians by mapping them onto the assemblies of well-understood quantum systems such as ultracold atoms in optical lattices, trapped ions or superconducting circuits. Semiconductor nanostructures which form the backbone of classical computing hold largely untapped potential for quantum simulation. In particular, chains of quantum dots in semiconductor nanowires can be used to emulate one-dimensional Hamiltonians such as the toy model of a topological p-wave superconductor. Here we realize a building block of this model, a double quantum dot w…
Understanding the spatial distribution of charge carriers in III-V nanowires proximity coupled to superconductors is important for the design and interpretation of experiments based on hybrid quantum devices. In this letter, the gate-dependent surface accumulation layer of InAsSb/Al nanowires was studied by means of Andreev interference in a parallel magnetic field. Both uniform hybrid nanowires and devices featuring a short Josephson junction fabricated by shadow lithography, exhibited periodic modulation of the switching current. The period corresponds to a flux quantum through the nanowire …
Epitaxially grown, high quality semiconductor InSb nanowires are emerging material systems for the development of high performance nanoelectronics and quantum information processing and communication devices, and for the studies of new physical phenomena in solid state systems. Here, we report on measurements of a superconductor-normal conductor-superconductor junction device fabricated from an InSb nanowire with aluminum based superconducting contacts. The measurements show a proximity induced supercurrent flowing through the InSb nanowire segment, with a critical current tunable by a gate, i…
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 InAs nanowire. We demonstrate coherent manipulation of these bound states, and track the bound-state …
We consider a system of two one-dimensional nanowires coupled via an $s$-wave superconducting strip, a geometry that is capable of supporting Kramers pairs of Majorana fermions. By performing an exact analytical diagonalization of a tunneling Hamiltonian describing the proximity effect (via a Bogoliubov transformation), we show that the excitation gap of the system varies periodically on the scale of the Fermi wavelength in the limit where the interwire separation is shorter than the superconducting coherence length. Comparing with the excitation gaps in similar geometries containing only dire…
We report on fabrication of single-electron transistors using InAs nanowires with epitaxial aluminium with fixed tunnel barriers made of aluminium oxide. The devices exhibit a hard superconducting gap induced by the proximized aluminium cover shell and they behave as metallic single-electron transistors. In contrast to the typical few channel contacts in semiconducting devices, our approach forms opaque multichannel contacts to a semiconducting wire and thus provides a complementary way to study them. In addition, we confirm that unwanted extra quantum dots can appear at the surface of the nan…
We report a method for making epitaxial superconducting contacts to semiconducting nanowires. The temperature and gate characteristics demonstrate barrier-free electrical contact, and the properties in the superconducting state are investigated at low temperature. Half-covering aluminum contacts are realized without the need of lithography and we demonstrate how to controllably insert high-band gap layers in the interface region. These developments are relevant to hybrid superconductor-nanowire devices that support Majorana zero energy states.
We study transport mediated by Andreev bound states formed in InSb nanowire quantum dots. Two kinds of superconducting source and drain contacts are used: epitaxial Al/InSb devices exhibit a doubling of tunneling resonances, while in NbTiN/InSb devices Andreev spectra of the dot appear to be replicated multiple times at increasing source-drain bias voltages. In both devices, a mirage of a crowded spectrum is created. To describe the observations a model is developed that combines the effects of a soft induced gap and of additional Andreev bound states both in the quantum dot and in the finite …
We experimentally study the electrical transport properties of Ge/Si core/shell nanowire device with two superconducting leads in the Coulomb blockade regime. Anomalous zero field magnetoconductance peaks are observed for the first time at the gate voltages where Coulomb blockade oscillation peaks present. Many evidences indicate this feature is due to Andreev reflection enhanced phase coherent single hole tunneling through the quantum dot, which can be suppressed by an external magnetic field without destroying the superconducting states in the electrodes.
We report measurements of the nonlinear conductance of InAs nanowire quantum dots coupled to superconducting leads. We observe a clear alternation between odd and even occupation of the dot, with sub-gap-peaks at $|V_{sd}|=Δ/e$ markedly stronger(weaker) than the quasiparticle tunneling peaks at $|V_{sd}|=2Δ/e$ for odd(even) occupation. We attribute the enhanced $Δ$-peak to an interplay between Kondo-correlations and Andreev tunneling in dots with an odd number of spins, and substantiate this interpretation by a poor man's scaling analysis.
Transport studies of Andreev bound states (ABSs) are complicated by the interplay of charging effects and superconductivity. Here, we compare transport approaches to ABS spectroscopy in a semiconductor-superconductor island to a charge-sensing approach based on an integrated radio-frequency single-electron transistor. Consistency of the methods demonstrates that fast, non-invasive charge sensing allows accurate quantitative measurement of ABSs while eluding some complexities of transport.
Demonstrating the topological protection of Andreev states in Josephson junctions is an experimental challenge. In particular the telltale $4π$ periodicity expected for the current phase relation of topological Josephson junctions has remained elusive, because of fast parity breaking processes. It was predicted that low temperature ac susceptibility measurements related to the current thermal noise could reveal the topological protection of quantum Spin Hall edge states \cite{Fu2009}, by probing their low energy Andreev spectrum.% of QSH-based Josephson junctions. We have performed such a micr…
A semiconducting nanowire fully wrapped by a superconducting shell has been proposed as a platform for obtaining Majorana modes at small magnetic fields. In this study, we demonstrate that the appearance of subgap states in such structures is actually governed by the junction region in tunneling spectroscopy measurements, and not the full-shell nanowire itself. Short tunneling regions never show subgap states, whereas longer junctions always do. This can be understood in terms of quantum dots forming in the junction and hosting Andreev levels in the Yu-Shiba-Rusinov regime. The intricate magne…
We analyze Andreev bound states (ABSs) that form in normal sections of a Rashba nanowire that is only partially covered by a superconducting layer. These ABSs are localized close to the ends of the superconducting section and can be pinned to zero energy over a wide range of magnetic field strengths even if the nanowire is in the non-topological regime. For finite-size nanowires (typically $\lesssim 1$ $μ$m in current experiments), the ABS localization length is comparable to the length of the nanowire. The probability density of an ABS is therefore non-zero throughout the nanowire and differe…
We study transport in a voltage biased superconductor-normal-superconductor (SNS) junction made of semiconducting nanowires with strong spin-orbit coupling, as it transitions into a topological superconducting phase for increasing Zeeman field. Despite the absence of a fractional steady-state ac Josephson current in the topological phase, the dissipative multiple Andreev reflection (MAR) current I_dc at different junction transparencies is particularly revealing. It exhibits unique features related to topology, such as the gap inversion, the formation of Majorana bound states, and fermion-pari…
Supercurrent and multiple Andreev reflections in Ge hut nanowire Josephson Junctions
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（凝聚态物理国家重点实验室和中国科学院物理研究所）
We present a Josephson junction based on a Ge-Si core-shell nanowire with transparent superconducting Al contacts, a building block which could be of considerable interest for investigating Majorana bound states, superconducting qubits and Andreev (spin) qubits. We demonstrate the dc Josephson effect in the form of a finite supercurrent through the junction, and establish the ac Josephson effect by showing up to 23 Shapiro steps. We observe multiple Andreev reflections up to the sixth order, indicating that charges can scatter elastically many times inside our junction, and that our interfaces…
Semiconductor quantum dots have proven to be a useful platform for quantum simulation in the solid state. However, implementing a superconducting coupling between quantum dots mediated by a Cooper pair has so far suffered from limited tunability and strong suppression. This has limited applications such as Cooper pair splitting and quantum dot simulation of topological Kitaev chains. In this work, we propose how to mediate tunable effective couplings via Andreev bound states in a semiconductor-superconductor nanowire connecting two quantum dots. We show that in this way it is possible to indiv…
We have performed microwave spectroscopy of Andreev states in superconducting weak links tailored in an InAs-Al (core-full shell) epitaxially-grown nanowire. The spectra present distinctive features, with bundles of four lines crossing when the superconducting phase difference across the weak link is 0 or $π.$ We interpret these as arising from zero-field spin-split Andreev states. A simple analytical model, which takes into account the Rashba spin-orbit interaction in a nanowire containing several transverse subbands, explains these features and their evolution with magnetic field. Our result…
Coupling individual atoms via tunneling fundamentally changes the state of matter: electrons bound to atomic cores become delocalized resulting in a change from an insulating to a metallic state, as it is well known from the canonical example of solids. A chain of atoms could lead to more exotic states if the tunneling takes place via the superconducting vacuum and can induce topologically protected excitations like Majorana or parafermions. Toward the realization of such artificial chains, coupling a single atom to the superconducting vacuum is well studied, but the hybridization of two sites…
We study theoretically the critical current in semiconductor nanowire Josephson junction with strong spin-orbit interaction. The critical current oscillates by an external magnetic field. We reveal that the oscillation of critical current depends on the orientation of magnetic field in the presence of spin-orbit interaction. We perform a numerical simulation for the nanowire by using a tight-binding model. The Andreev levels are calculated as a function of phase difference $φ$ between two superconductors. The DC Josephson current is evaluated from the Andreev levels in the case of short juncti…
We investigate superconducting quantum interference devices consisting of two highly transmissive Josephson junctions coupled by a superconducting loop, all defined in an epitaxial InAs/Al heterostructure. A novel device design allows for independent measurements of the Andreev bound state spectrum within the normal region of a junction and the resulting current-phase relation. We show that knowledge of the Andreev bound state spectrum alone is enough to derive the independently measured phase dependent supercurrent. On the other hand, the opposite relation does not generally hold true as deta…
In this PhD thesis, quantum devices based on molecular-beam epitaxy grown InAs semiconductor with an in-situ grown epitaxial Al film were investigated. Novel device geometries were realized that allow for the study of bound states that emerge at low temperatures in semiconducting nanowires due to the presence of spin-orbit coupling, Zeeman effect, and superconducting proximity effect. Experiments utilizing either gate-defined nanowires in two-dimensional heterostructures or vapor-liquid-solid grown nanowires with a full-shell of Al are presented. Devices and experimental methods were developed…
Many present and future applications of superconductivity would benefit from electrostatic control of carrier density and tunneling rates, the hallmark of semiconductor devices. One particularly exciting application is the realization of topological superconductivity as a basis for quantum information processing. Proposals in this direction based on proximity effect in semiconductor nanowires are appealing because the key ingredients are currently in hand. However, previous instances of proximitized semiconductors show significant tunneling conductance below the superconducting gap, suggesting…
Gate-controlled supercurrent (GCS) in superconductor nanobridges has recently attracted attention as a means to create superconducting field effect transistors. Despite the clear advantage for applications with low power consumption and high switching speeds, the microscopic mechanism of the field effect is still under debate. In this work, we realize GCS for the first time in an epitaxial superconductor, which is created as a shell on an InAs nanowire. We show that the supercurrent in the epitaxial Al layer can be switched to the normal state by applying $\simeq\pm$ 23$\,$V on a bottom gate i…
We study the proximity effect in a topological nanowire tunnel coupled to an s-wave superconducting substrate. We use a general Green's function approach that allows us to study the evolution of the Andreev bound states in the wire into Majorana fermions. We show that the strength of the tunnel coupling induces a topological transition in which the Majorana fermionic states can be destroyed when the coupling is very strong. Moreover, we provide a phenomenologial study of the effects of disorder in the superconductor on the formation of Majorana fermions. We note a non-trivial effect of a quasi…
We investigate theoretically the Josephson junction of semiconductor nanowire with strong spin-orbit (SO) interaction in the presence of magnetic field. By using a tight-binding model, the energy levels $E_n$ of Andreev bound states are numerically calculated as a function of phase difference $φ$ between two superconductors in the case of short junctions. The DC Josephson current is evaluated from the Andreev levels. In the absence of SO interaction, a $0$-$π$ transition due to the magnetic field is clearly observed. In the presence of SO interaction, the coexistence of SO interaction and Zeem…
The combination of strong spin-orbit coupling, large $g$-factors, and the coupling to a superconductor can be used to create a topologically protected state in a semiconductor nanowire. Here we report on growth and characterization of hybrid epitaxial InAsSb/Al nanowires, with varying composition and crystal structure. We find the strongest spin-orbit interaction at intermediate compositions in zincblende InAs$_{1-x}$Sb$_{x}$ nanowires, exceeding that of both InAs and InSb materials, confirming recent theoretical studies \cite{winkler2016topological}. We show that the epitaxial InAsSb/Al inter…
We study experimentally the low temperature resistance of superconducting nanowires connected to normal metal reservoirs. We find that a substantial fraction of the nanowires is resistive, down to the lowest temperature measured, indicative of an intrinsic boundary resistance due to the Andreev-conversion of normal current to supercurrent. The results are successfully analyzed in terms of the kinetic equations for diffusive superconductors.
Hybrid system composed by a semiconducting nanowire with proximity-induced superconductivity and a quantum dot at the end working as spectrometer was recently used to quantify the so-called degree of Majorana nonlocality [Deng et al., Phys.Rev.B, 98, 085125 (2018)]. Here we demonstrate that spin-resolved density of states of the dot responsible for zero-bias conductance peak strongly depends on the separation between the Majorana bound states (MBSs) and their relative couplings with the dot and investigate how the charging energy affects the spectrum of the system in the distinct scenarios of …
Coulomb blockaded transport of topological superconducting nanowires provides an opportunity to probe the localization of states at both ends of the system in a two-terminal geometry. In addition, it provides a way for checking for subgap states away from the leads. At the same time, Coulomb blockade transport is difficult to analyze because of the interacting nature of the problem arising from the nonperturbative Coulomb interaction inherent in the phenomenon. Here we show that the Coulomb blockade transport can be modeled at the same level of complexity as quantum point contact tunneling tha…
A semiconductor nanowire based superconductor-normal-superconductor (SNS) junction is modeled theoretically. A magnetic field is applied along the nanowire axis, parallel to the current. The Bogoliubov-de Gennes equations for Andreev bound states are solved while considering the electronic subbands due to radial confinement in the N-section. The energy-versus-phase curves of the Andreev bound states shift in phase as the N-section quasiparticles with orbital angular momentum couple to the axial field. A similar phase shift is observed in the continuum current of the junction. The quantum mecha…
In modern experiments with hybrid superconducting (SC)/semiconducting nanowires the presence of zero-energy Andreev bound states (ABSs), characterized by a partial overlap of the Majorana wave functions, is a common problem that significantly complicates the detection of a genuine Majorana bound state (MBS). In this article, taking into account spatial inhomogeneity of experimentally investigated nanowire samples, we study interference transport features of a curved heterostructure in which two normal wires (or arms) are separated by a superconducting wire. Since Andreev reflection on the two …
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 tri…
Semiconductor-superconductor hybrids are widely used for realising complex quantum phenomena such as topological superconductivity and spins coupled to Cooper pairs. Accessing exotic regimes at high magnetic fields and increasing operating temperatures beyond the state-of-the-art requires new, epitaxially matched semiconductor-superconductor materials. The challenge is to generate favourable conditions for heterostructure formation between materials with the desired inherent properties. Here, we harness increased knowledge of metal-on-semiconductor growth to develop InAs nanowires with epitaxi…
Quantifying the non-Abelian property of Andreev bound states in inhomogeneous Majorana nanowires
School of Physics, MOE Key Laboratory for Non-equilibrium Synthesis and Modulation of Condensed Matter, Xi’an Jiaotong University（西安交通大学物理学院，非平衡合成与调控凝聚态物质教育部重点实验室）；Interdisciplinary Center for Theoretical Physics and Information Sciences, Fudan University（复旦大学理论物理与信息科学交叉中心）；Hefei National Laboratory（合肥国家实验室）；International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）
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