Semiconductor-superconductor Nanowires Research Articles

Shadowed versus Etched Superconductor-Semiconductor Junctions in Al/InAs Nanowires.

Hybrid semiconductor-superconductor nanowires have emerged as a cornerstone in modern quantum devices. Integrating such nanowires into hybrid devices typically requires extensive postgrowth processing which may affect device performance unfavorably. Here, we present a technique for in situ shadowing superconductors on nanowires and compare the structural and electronic properties of Al junctions formed by shadowing versus etching. Based on transmission electron microscopy, we find that typical etching procedures lead to atomic-scale surface roughening. This surface perturbation may cause a reduction of the electron mobility as demonstrated in transport measurements. Further, we display advanced shadowing geometries aiding in the pursuit of bringing fabrication of hybrid devices in situ. Finally, we give examples of shadowed junctions exploited in various device geometries that exhibit high-quality quantum transport signatures.

Spin-filtered measurements of Andreev bound states in semiconductor-superconductor nanowire devices

Semiconductor nanowires coupled to superconductors can host Andreev bound states with distinct spin and parity, including a spin-zero state with an even number of electrons and a spin-1/2 state with odd-parity. Considering the difference in spin of the even and odd states, spin-filtered measurements can reveal the underlying ground state. To directly measure the spin of single-electron excitations, we probe an Andreev bound state using a spin-polarized quantum dot that acts as a bipolar spin filter, in combination with a non-polarized tunnel junction in a three-terminal circuit. We observe a spin-polarized excitation spectrum of the Andreev bound state, which can be fully spin-polarized, despite strong spin-orbit interaction in the InSb nanowires. Decoupling the hybrid from the normal lead causes a current blockade, by trapping the Andreev bound state in an excited state. Spin-polarized spectroscopy of hybrid nanowire devices, as demonstrated here, is proposed as an experimental tool to support the observation of topological superconductivity.

Sn/InAs Josephson Junctions on Selective Area Grown Nanowires with in Situ Shadowed Superconductor Evaporation.

Superconductor-semiconductor nanowire hybrid structures are useful in fabricating devices for quantum information processing. While selective area growth (SAG) offers the flexibility to grow semiconductor nanowires in arbitrary geometries, in situ evaporation of superconductors ensures pristine superconductor-semiconductor interfaces, resulting in strong induced superconductivity in the semiconducting nanowire. In this work, we used high-aspect-ratio SiOx dielectric walls to in situ evaporate islands of superconductor tin on in-plane InAs SAG nanowires. Our technique enables customization in the designs of such hybrid nanostructures, while simultaneously performing the nanowire and superconductor growth without breaking vacuum. Using this technique, we grew super(S)-normal(N)-super(S), NS, and SNSNS junctions. We performed cryogenic electron transport measurements revealing the presence of gate and field tunable supercurrents. We further measured the superconducting gap and critical fields in the hybrid nanostructures and the crossover from 2e to 1e periodicity in the SNSNS junctions as a proof of the usability of these hybrid nanostructures.

Delocalized states in three-terminal superconductor-semiconductor nanowire devices

We fabricate three-terminal hybrid devices consisting of a semiconductor nanowire segment proximitized by a grounded superconductor and having tunnel probe contacts on both sides. By performing simultaneous tunneling measurements, we identify delocalized states, which can be observed from both ends, and states localized near one of the tunnel barriers. The delocalized states can be traced from zero magnetic field to fields beyond 0.5 T. Within the regime that supports delocalized states, we search for correlated low-energy features consistent with the presence of Majorana zero modes. While both sides of the device exhibit ubiquitous low-energy features at high fields, no correlation is inferred. Simulations using a one-dimensional effective model suggest that the delocalized states, which extend throughout the whole system, have large characteristic wave vectors, while the lower momentum states expected to give rise to Majorana physics are localized by disorder. To avoid such localization and realize Majorana zero modes, disorder needs to be reduced significantly. We propose a method for estimating the disorder strength based on analyzing the level spacing between delocalized states.

Epitaxially Driven Phase Selectivity of Sn in Hybrid Quantum Nanowires.

Hybrid semiconductor-superconductor nanowires constitute a pervasive platform for studying gate-tunable superconductivity and the emergence of topological behavior. Their low dimensionality and crystal structure flexibility facilitate unique heterostructure growth and efficient material optimization, crucial prerequisites for accurately constructing complex multicomponent quantum materials. Here, we present an extensive study of Sn growth on InSb, InAsSb, and InAs nanowires and demonstrate how the crystal structure of the nanowires drives the formation of either semimetallic α-Sn or superconducting β-Sn. For InAs nanowires, we observe phase-pure superconducting β-Sn shells. However, for InSb and InAsSb nanowires, an initial epitaxial α-Sn phase evolves into a polycrystalline shell of coexisting α and β phases, where the β/α volume ratio increases with Sn shell thickness. Whether these nanowires exhibit superconductivity or not critically relies on the β-Sn content. Therefore, this work provides key insights into Sn phases on a variety of semiconductors with consequences for the yield of superconducting hybrids suitable for generating topological systems.

Electrostatic control of the proximity effect in the bulk of semiconductor-superconductor hybrids

The proximity effect in semiconductor-superconductor nanowires is expected to generate an induced gap in the semiconductor. The magnitude of this induced gap, together with the semiconductor properties like spin-orbit coupling and g-factor, depends on the coupling between the materials. It is predicted that this coupling can be adjusted through the use of electric fields. We study this phenomenon in InSb/Al/Pt hybrids using nonlocal spectroscopy. We show that these hybrids can be tuned such that the semiconductor and superconductor are strongly coupled. In this case, the induced gap is similar to the superconducting gap in the Al/Pt shell and closes only at high magnetic fields. In contrast, the coupling can be suppressed which leads to a strong reduction of the induced gap and critical magnetic field. At the crossover between the strong-coupling and weak-coupling regimes, we observe the closing and reopening of the induced gap in the bulk of a nanowire. Contrary to expectations, it is not accompanied by the formation of zero-bias peaks in the local conductance spectra. As a result, this cannot be attributed conclusively to the anticipated topological phase transition and we discuss possible alternative explanations.

Recent progress on Majorana in semiconductor-superconductor heterostructures—engineering and detection

Majorana zero modes (MZMs) are exotic excitations (in condensed matter systems) that have potential applications in topological quantum computation. Though MZMs have been predicted on many platforms, their existence of them is still under debate. In this paper, we review the recent progress of engineering and detecting MZMs in semiconductor-superconductor heterostructures. We also briefly review the protocols of implementing topological quantum computation by hybrid semiconductor-superconductor nanowires.

Tunable Superconducting Coupling of Quantum Dots via Andreev Bound States in Semiconductor-Superconductor Nanowires.

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 Letter, 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 individually control both the coupling mediated by Cooper pairs and by single electrons by changing the properties of the Andreev bound states with easily accessible experimental parameters. In addition, the problem of coupling suppression is greatly mitigated. We also propose how to experimentally extract the coupling strengths from resonant current in a three-terminal junction. Our proposal will enable future experiments that have not been possible so far.

Selective Area Growth of PbTe Nanowire Networks on InP

AbstractHybrid semiconductor–superconductor nanowires are promising candidates as quantum information processing devices. The need for scalability and complex designs calls for the development of selective area growth techniques. Here, the growth of large scale lead telluride (PbTe) networks is introduced by molecular beam epitaxy. The group IV‐VI lead‐salt semiconductor is an attractive material choice due to its large dielectric constant, strong spin‐orbit coupling, and high carrier mobility. A crystal re‐orientation process during the initial growth stages leads to single crystalline nanowire networks despite a large lattice mismatch, different crystal structure, and diverging thermal expansion coefficient to the indium phosphide (InP) substrate. The high quality of the resulting material is confirmed by Hall bar measurements, indicating mobilities up to 5600 cm2 (Vs)−1, and Aharonov–Bohm experiments, indicating a low‐temperature phase coherence length exceeding 21 µm. Together, these properties show the high potential of the system as a basis for topological networks.

Magnetic field constraint for Majorana zero modes in a hybrid nanowire

The hybrid semiconductor-superconductor nanowire is expected to serve as an experimental platform to support Majorana zero modes. By rederiving its effective Kitaev model with spins, we discover a topological phase diagram, which assigns a more precise constraint on the magnetic field strength for the emergence of Majorana zero modes. We find that the effective pairing strength dressed by the proximity effect exhibits a significant dependence on the magnetic field, and thus the topological phase region is refined into a closed triangle in the phase diagram with chemical potential vs Zeeman energy (which is obviously different from the open hyperbolic region known before). This prediction is confirmed again by an exact calculation of quantum transport, where the zero bias peak of $2{e}^{2}/h$ in the differential conductance spectrum, as the necessary evidence for the Majorana zero modes, disappears when the magnetic field grows too strong. Therefore, the hybrid nanowire system does not support Majorana zero modes under a too strong magnetic field. For illustrations with practical hybrid systems, in the InSb nanowire coupled to NbTiN, the accessible magnetic field range is around 0.1--1.5 T; when coupled to an aluminum shell, the accessible magnetic field range should be smaller than 0.12 T. Our predictions are essential to significantly narrow down the range of magnetic fields for further searching Majorana zero modes in experiments.

Large zero bias peaks and dips in a four-terminal thin InAs-Al nanowire device

We report electron transport studies of a thin InAs-Al hybrid semiconductor-superconductor nanowire device using a four-terminal design. Compared to previous works, thinner InAs nanowire (diameter less than 40 nm) is expected to reach fewer sub-band regime. The four-terminal device design excludes electrode contact resistance, an unknown value which has inevitably affected previously reported device conductance. Using tunneling spectroscopy, we find large zero-bias peaks (ZBPs) in differential conductance on the order of $2e^2/h$. Investigating the ZBP evolution by sweeping various gate voltages and magnetic field, we find a transition between a zero-bias peak and a zero-bias dip while the zero-bias conductance sticks close to $2e^2/h$. We discuss a topologically trivial interpretation involving disorder, smooth potential variation and quasi-Majorana zero modes.

Random matrix theory for the robustness, quantization, and end-to-end correlation of zero-bias conductance peaks in a class D ensemble

We develop a general theory to study strong random quenched disorder effects in systems of experimental relevance in the search for Majorana zero modes in topological superconductors. Using the random matrix theory in a class D ensemble, we simulate the transport properties of random quantum dots by attaching leads, and calculating the differential conductance in the $S$-matrix formalism. To add the concept of the length to the random system so that disordered Majorana nanowires can be simulated by the random matrix theory, we generalize the model of a single quantum dot to a chain of quantum dots by analogy with the superconductor-semiconductor nanowire Majorana platform. We first define a new concept, the robustness of zero-bias conductance peaks, in terms of an effective random Hamiltonian considering the self-energy of leads. We then study the joint distribution for the robustness and zero-bias conductance peaks, and find a strong correlation that the zero-bias conductance peak with stronger robustness is also prone to carry a larger conductance peak near $2{e}^{2}/h$. This trend is more prominent in shorter chains than in longer chains. This is consistent with experimentally observed zero-bias conductance associated with disorder-induced trivial Andreev bound states (the so-called ugly zero-bias peaks). Finally, we study the end-to-end correlation of the disorder-induced zero-bias conductances from two leads by calculating the normalized mutual information, which estimates the degrees of the correlation arising from the trivial zero-bias conductance peaks. Our work provides an estimate of several important metrics used in superconductor-semiconductor experiments to determine the nature of zero-bias conductance peaks, including the robustness, the quantization, and the end-to-end correlation of the trivial zero-bias peaks. Therefore, in order to claim any evidence for the Majorana zero modes, one must establish the observed zero-bias conductance peaks to have considerable statistical significance well beyond what we find in this work to exist for the trivial peaks.

Non-Hermiticity-stabilized Majorana zero modes in semiconductor-superconductor nanowires

Coupled Majorana zero modes with nonzero energies are generally detrimental to the non-Abelian statistics due to the additional dynamic phase. Nevertheless, we show that a well-connected lead can introduce a local non-Hermitian dissipation term to shift the energies of both coupled Majorana modes to zero, and surprisingly turn the coupled Majorana mode far from the lead into a dark Majorana mode with exponentially small dissipation. This dark Majorana mode can conquer the drawback of the partially overlapped Majorana zero modes and possess the properties of true Majorana zero mode such as the perfect fractional Josephson effect and the non-Abelian statistics.

Edge-State Oscillations in a One-Dimensional Topological Chain with Dissipative Couplings

The edge states in a one-dimensional Su-Schrieffer-Heeger (SSH) chain have been extensively studied for their topologically protected properties when there are onsite dissipations induced by independent environments. We here show that common environments shared by nearest neighboring sites in the SSH chain can result in dissipative couplings between sites, and thus change the topologically trivial phase to a nontrivial one. In contrast to usual hybridization of two edge states in the SSH chain with finite size, we find that the dissipative couplings result in oscillations of these hybridized edge states, which are similar to those of Majorana modes in the semiconductor-superconductor nanowire. The parameter for controlling the topological phase of the SSH chain plays the role of the magnetic field in a nanowire for controlling Majorana oscillation. A measurement method for oscillations is proposed. Our study provides a useful way to manipulate and ascertain edge states, and is experimentally feasible within current technology of superconducting quantum circuits.

Observation of Aharonov-Bohm effect in PbTe nanowire networks

We report phase coherent electron transport in PbTe nanowire networks with a loop geometry. Magnetoconductance shows Aharonov-Bohm (AB) oscillations with periods of $h/e$ and $h/2e$ in flux. The amplitudes of $h/2e$ oscillations are enhanced near zero magnetic field, possibly due to interference between time-reversal paths. Temperature dependence of the AB amplitudes suggests a phase coherence length $\ensuremath{\sim}8\text{}12\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$ at 50 mK. This length scale is larger than the typical geometry of PbTe-based hybrid semiconductor-superconductor nanowire devices.

Suppressing Andreev Bound State Zero Bias Peaks Using a Strongly Dissipative Lead.

Hybrid semiconductor-superconductor nanowires are predicted to host Majorana zero modes that induce zero-bias peaks (ZBPs) in tunneling conductance. ZBPs alone, however, are not sufficient evidence due to the ubiquitous presence of Andreev bound states. Here, we implement a strongly resistive normal lead in InAs-Al nanowire devices and show that most of the expected Andreev bound state-induced ZBPs can be suppressed, a phenomenon known as environmental Coulomb blockade. Our result is the first experimental demonstration of this dissipative interaction effect on Andreev bound states and can serve as a possible filter to narrow down the ZBP phase diagram in future Majorana searches.

Non-Abelian statistics of Majorana zero modes in the presence of an Andreev bound state

Braiding Majorana zero modes (MZMs) is the key procedure toward topological quantum computation. We show such braiding can be well performed in a parallel semiconductor-superconductor nanowire structure. Considering the fact that the low-energy Andreev bound states (ABSs) usually mix with the MZMs in the present setup, we further investigate the braiding properties of MZMs when an ABS is presented. Our numerical simulation suggests that ABS can be regarded as a pair of weakly coupled MZMs. The dynamical hybridization of MZMs plus the non-Abelian braiding of MZMs would induce an arbitrary rotation on the Bloch sphere of a single qubit. Remarkably, such rotation is manipulable since the rotation parameters could be individually modulated. Thus, the dynamic evolution can be eliminated and the non-Abelian braiding statistics, independent of the braiding time, retrieves.

Weyl points in multiterminal hybrid superconductor-semiconductor nanowire devices

The technology of superconductor-semiconductor nanowire devices has matured in the last years in the course of Majorana research. This makes it feasible to design more complex and sophisticated devices. The authors investigate multiterminal superconductor-semiconductor wires to probe the feasibility of another topological phenomenon, namely, Weyl singularities in their Andreev spectrum. They discover an abundance of Weyl singularities for devices with intermediate spacing between the electrodes.

Estimating disorder and its adverse effects in semiconductor Majorana nanowires

We use the available transport measurements in the literature to develop a dataset for the likely amount of disorder in semiconductor (InAs and InSb) materials which are used in fabricating the superconductor-semiconductor nanowire samples in the experimental search for Majorana zero modes. Using the estimated disorder in direct Majorana simulations, we conclude that the current level of disorder in semiconductor Majorana nanowires is at least an order of magnitude higher than that necessary for the emergence of topological Majorana zero modes. In agreement with existing results, we find that our estimated disorder leads to the occasional emergence of trivial zero modes, which can be post-selected and then further fine-tuned by varying system parameters (e.g., tunnel barrier), leading to trivial zero-bias conductance peaks in tunneling spectroscopy with $ \sim 2e^2/h $ magnitude. Most calculated tunnel spectra in these disordered systems, however, manifest essentially no significant features, which is also consistent with the current experimental status, where zero-bias peaks are found only occasionally in some samples under careful fine-tuning.

Crossover between trivial zero modes in Majorana nanowires

We consider the superconductor-semiconductor nanowire hybrid Majorana platform ("Majorana nanowire") in the presence of a deterministic spatially slowly varying inhomogeneous chemical potential and a random spatial quenched potential disorder, both of which are known to produce nontopological almost-zero-energy modes mimicking the theoretically predicted topological Majorana zero modes. We study the crossover among these mechanisms by calculating the tunnel conductance while varying the relative strength between inhomogeneous potential and random disorder in a controlled manner. We find that the entire crossover region manifests abundant trivial zero modes, many of which showing the apparent "quantization" of the zero-bias conductance peak at $ 2e^2/h $, with occasional disorder-dominated peaks exceeding $ 2e^2/h $. We present animations of the simulated crossover behavior and discuss experimental implications. Additionally, in order to simulate the realistic disorder in experimental nanowires, we also study in depth the case of disorder arising from random individual static impurities along the wire, and consider crossover associated with such impurity effects. Our results, when compared qualitatively with existing Majorana nanowire experimental results, indicate the dominant role of random disorder in the experiments. It turns out that all three mechanisms may produce trivial zero-bias peaks in the tunnel conductance, and the crossover among these physical mechanisms (i.e., when more than one mechanism is present in the system) is smooth and continuous, making it difficult a priori to conclude which mechanism is dominant in a particular sample just by a casual inspection of the zero-bias conductance peaks.