arXiv subjects

Tudor D. Stanescu

Publications and source records attributed to Tudor D. Stanescu.

At least 37 records · Page 2Linked to original sources

arXiv2019

Subband occupation in semiconductor-superconductor nanowires

Subband occupancy (i.e. the number of occupied subbands or energy levels in the semiconductor) is a key physical parameter characterizing the topological properties of superconductor-semiconductor hybrid systems in the context of the search for non-Abelian Majorana zero modes. We theoretically study the subband occupation of semiconductor nanowire devices as function of the applied gate potential, the semiconductor-superconductor (SM-SC) work function difference, and the surface charge density by solving self-consistently the Schrödinger-Poisson equations for the conduction electrons of the semiconductor nanowire. Realistic surface charge densities, which are responsible for band bending, are shown to significantly increase the number of occupied subbands, making it difficult or impossible to reach a regime where only a few subbands are occupied. We also show that the energy separation between subbands is significantly reduced in the regime of many occupied subbands, with highly detrimental consequences for the realization and observation of robust Majorana zero modes. As a consequence, the requirements for the realization of robust topological superconductivity and Majorana zero modes should include a low value of the chemical potential, consistent with the occupation of only a few subbands. Finally, we show that the local density of states on the exposed nanowire facets provides a powerful tool for identifying a regime with many occupied subbands and is capable of providing additional critical information regarding the feasibility of Majorana physics in semiconductor-superconductor devices. In our work, we address both InAs/Al and InSb/Al superconductor-nanowire hybrid systems of current experimental interest.

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arXiv2019

Curvature of gap closing features and the extraction of Majorana nanowire parameters

Recent tunneling conductance measurements of Majorana nanowires show a strong variation in the magnetic field dependence of the superconducting gap among different devices. Here, we theoretically study the magnetic field dependence of the gap closing feature and establish that the degree of convexity (or concavity) of the gap closing as a function of Zeeman field can provide critical constraints on the underlying microscopic parameters of the semiconductor-superconductor hybrid system model. Specifically, we show that the gap closing feature is entirely concave only for strong spin-orbit coupling strength relative to the chemical potential. Additionally, the non-linearity (i.e. concavity or convexity) of the gap closing as a function of magnetic field complicates the simple assignment of a constant effective $ g $-factor to the states in the Majorana nanowire. We develop a procedure to estimate the effective $ g $-factor from recent experimental data that accounts for the non-linear gap closing resulting from the interplay between chemical potential and spin-orbit coupling. Thus, measurements of the magnetic field dependence of the gap closure on the trivial side of the topological quantum phase transition can provide useful information on parameters that are critical to the theoretical modeling of Majorana nanowires.

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arXiv2019

Zero-energy pinning of topologically-trivial bound states in multi-band semiconductor-superconductor nanowires

Recent tunneling conductance measurements on semiconductor-superconductor nanowires find zero-bias peaks to be ubiquitous across wide ranges of chemical potential and Zeeman energy. Motivated by this, we demonstrate that topologically-trivial Andreev abound states (ABSs) pinned near zero energy are produced rather generically in inhomogeneous systems with multi-band occupancy in the presence of inter-band coupling. We first investigate the inter-band coupling mechanism responsible for the pinning within a multi-band 1D toy model, then we confirm the findings using a 3D Schrödinger-Poisson approach that incorporates the geometric and electrostatic details of the actual device. Our analysis shows that level-repulsion generated by inter-band coupling can lead to a rather spectacular pinning of the lowest-energy mode near zero energy in systems (or regions) characterized by very-short length scales ($\sim100~$nm).We show that level repulsion between the lowest energy levels can mimic the gap opening feature (simultaneous with the emergence of a near-zero energy mode) predicted to occur in Majorana hybrid systems. We also demonstrate that nearly-zero bias differential conductance features exhibiting particle-hole asymmetry are due to the presence of (topologically-trivial) ABSs pinned near zero-energy by level repulsion, not to Majorana zero modes, quasi-Majoranas, or any other low-energy mode that involves (partially) separated Majorana bound states. Our findings demonstrate the importance of understanding in detail multi-band physics and electrostatic effects in the context of the ongoing search for Majorana modes in semiconductor-superconductor heterostructures.

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arXiv2019

Electronic structure of full-shell InAs/Al hybrid semiconductor-superconductor nanowires: Spin-orbit coupling and topological phase space

We study the electronic structure of full-shell superconductor-semiconductor nanowires, which have recently been proposed for creating Majorana zero modes, using an eight-band $\vec{k} \cdot \vec{p}$ model within a fully self-consistent Schrödinger-Poisson scheme. We find that the spin-orbit coupling induced by the intrinsic radial electric field is generically weak for sub-bands with their minimum near the Fermi energy. Furthermore, we show that the chemical potential windows consistent with the emergence of a topological phase are small and sparse and can only be reached by fine tunning the diameter of the wire. These findings suggest that the parameter space consistent with the realization of a topological phase in full-shell InAs/Al nanowires is, at best, very narrow.

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arXiv2019

Conductance feature smearing and anisotropic suppression of induced superconductivity in a Majorana nanowire

In a recent high-quality experimental work on normal metal--superconducting nanowire junctions arXiv:1807.01940 (2018), strong anisotropic suppression of induced superconductivity has been observed in tunnel conductance measurements in the presence of applied magnetic field with variable orientation. Following this finding, we investigate theoretically the dependence of tunnel conductance on the direction of the Zeeman field in order to understand the operational mechanisms and to extract effective system parameters. Second, motivated by a generic discrepancy between experiment and theory, i.e., many in-gap and above-gap conductance features predicted by theory are barely observed in experiments, we study several mechanisms possibly responsible for the suppression of the theoretically predicted conductance features (e.g., length of the nanowire, self-energy effect due to the proximity effect, finite temperature, finite dissipation, and multiband effect). One essential finding in the current work is that only by a combined understanding of both suppression mechanisms can we extract effective system parameters from the experimental data (e.g., the effective nanowire-superconductor coupling, the effective Landé $g$ factor, and the chemical potential of the semiconducting nanowire). In addition, we consider topologically trivial Andreev bound states in hybrid nanowires in the presence of potential inhomogeneities, such as external quantum dots or potential inhomogeneities inside the nanowire. We compare the anisotropic, field-dependent features induced by these nontopological Andreev bound states with the corresponding features produced by topological Majorana zero modes in pristine nanostructures, so that we can provide guidance to differentiate between the topologically trivial and nontrivial cases.

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arXiv2018

Quasiparticle gaps in multiprobe Majorana nanowires

We theoretically study a spin-orbit-coupled nanowire proximitized by a superconductor in the presence of an externally applied Zeeman field ("Majorana nanowire") with zero-energy Majorana bound states localized at the two ends of the wire when the Zeeman spin splitting is large enough for the system to enter the topological phase. The specific physics of interest in the current work is the effect of having several tunnel probes attached to the wire along its length. Such tunnel probes should allow, as a matter of principle, one to observe both the predicted bulk superconducting gap closing and opening associated with the topological quantum phase transition as well as the Majorana bound states at the wire ends showing up as zero-bias conductance peaks, depending on which probes are used for the tunneling spectroscopy measurement. Because of the possible invasive nature of the tunnel probes, producing local potential fluctuations in the nanowire, we find the physical situation to be quite complex. In particular, depending on the details of the tunnel barrier operational at the probes, the Majorana nanowire could manifest additional low-energy Andreev bound states which will manifest their own almost-zero-bias peaks, complicating the interpretation of the tunneling data in multiprobe Majorana nanowires. We use two complementary microscopic models to simulate the probes, finding that the tunneling conductance spectrum depends rather sensitively on the details of the tunnel barriers at the probes. We apply our general analysis to simulate a recent multiprobe nanowire experiment commenting on the nature of the quasiparticle gaps likely controlling the experimental observations.

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arXiv2018

Metamorphosis of Andreev bound states into Majorana bound states in pristine nanowires

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, in agreement with most recent experimental observations. The gap closure feature is actually the coming together of the Andreev bound states at high chemical potential rather than a simple trivial gap of extended bulk states closing at the transition. Our theoretical finding establishes the generic intrinsic Andreev bound states on the trivial side of the topological quantum phase transition as the main contributors to the tunneling conductance spectra, providing a generic interpretation of existing experiments in clean Majorana nanowires. Our work also explains why experimental tunnel conductance spectra generically have gap closing features below the topological quantum phase transition, but no gap opening features above it.

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arXiv2018

Control and detection of Majorana bound states in quantum dot arrays

We study the low-energy physics of a one-dimensional array of superconducting quantum dots realized by proximity coupling a semiconductor nanowire to multiple superconducting islands separated by narrow uncovered regions. The effective electrostatic potential inside the quantum dots and the uncovered regions can be controlled using potential gates. By performing detailed numerical calculations based on effective tightbinding models, we find that multiple low-energy sub-gap states consisting of partially overlapping Majorana bound states emerge generically in the vicinity of the uncovered regions. Explicit differential conductance calculations show that a robust zero-bias conductance peak is not inconsistent with the presence of such states localized throughout the system, hence the observation of such a peak does not demonstrate the realization of well-separated Majorana zero modes. However, we find that creating effective potential wells in the uncovered regions traps pairs of nearby partially overlapping Majorana bound states, which become less separated and acquire a finite gap that protects the pair of Majorana zero modes localized at the ends of the system. This behavior persists over a significant parameter range, suggesting that proximitized quantum dot arrays could provide a platform for highly controllable Majorana devices.

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arXiv2018

Kitaev chain with a quantum dot

We solve analytically the problem of a finite length Kitaev chain coupled to a quantum dot (QD), which extends the standard Kitaev chain problem making it more closely related to the quantum dot-semiconductor-superconductor (QD-SM-SC) nanowire heterostructure that is currently under intense investigation for possible occurrence of Majorana zero modes (MZMs). Our analytical solution reveals the emergence of a robust Andreev bound state (ABSs) localized in the quantum dot region as the generic lowest energy solution in the topologically trivial phase. By contrast, in the bare Kitaev chain problem such a solution does not exist. The robustness of the ABS in the topologically trivial phase is due to a partial decoupling of the component Majorana bound states (MBSs) over the length of the dot potential. As a result, the signatures of the ABS in measurements that couple locally to the quantum dot, e.g., tunneling measurements, are identical to the signatures of topologically-protected MZMs, which arise only in the topological superconducting (TS) phase of the Kitaev chain.

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arXiv2018

Effective theory approach to the Schrodinger-Poisson problem in semiconductor Majorana devices

We propose a method for solving the Schrodinger-Poisson problem that can be efficiently implemented in realistic 3D tight-binding models of semiconductor-based Majorana devices. The method is based on two key ideas: i) For a given geometry, the Poisson problem is only solved once (for each local orbital) and the results are stored as an interaction tensor; using this Green's function scheme, the Poisson component of the iteration procedure is reduced to a few simple summations. ii) The 3D problem is mapped into an effective multi-orbital 1D problem with molecular orbitals calculated self-consistently as the transverse modes of an infinite wire with the same electrostatic potential as the local electrostatic potential of the finite 3D device. To demonstrate the capabilities of our approach, we calculate the response of the system to an external magnetic field, the dependence of the effective chemical potential on the work function difference, and the dependence of the effective semiconductor-superconductor coupling on the applied gate potential. We find that different low-energy bands are characterized by similar effective couplings, which results in induced gap features characterized by a single energy scale. We also find that electrostatic effects are responsible for a partial suppression of the Majorana energy splitting oscillations. Finally, we show that a position-dependent work function difference can produce a non-homogeneous effective potential that is not affected by the screening due to the superconductor and is only partially suppressed by the charge inside the wire. In turn, this potential can induce trivial low-energy states that mimic the phenomenology of Majorana zero modes. Thus, any position-dependent work function difference (even at the 1% level) along the nanowire must be avoided through carefully engineered semiconductor-superconductor interfaces.

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arXiv2018

Robust topological phase in proximitized core-shell nanowires coupled to multiple superconductors

We consider core-shell nanowires with prismatic geometry contacted with two or more superconductors in the presence of a magnetic field applied parallel to the wire. In this geometry, the lowest energy states are localized on the outer edges of the shell, which strongly inhibits the orbital effects of the longitudinal magnetic field that are detrimental to Majorana physics. Using a tight-binding model of coupled parallel chains, we calculate the topological phase diagram of the hybrid system in the presence of non-vanishing transverse potentials and finite relative phases between the parent superconductors. We show that having finite relative phases strongly enhances the stability of the induced topological superconductivity over a significant range of chemical potentials and reduces the value of the critical field associated with the topological quantum phase transition.

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arXiv2018

Building topological quantum circuits: Majorana nanowire junctions

Topological quantum computation using non-Abelian Majorana zero modes localized in proximitized semiconductor nanowires requires careful electrostatic control of wire-junctions so as to manipulate and braid the zero modes enabling anyonic fault-tolerant gate operations. We theoretically investigate the topological superconducting properties of such elementary wire-junctions, the so-called T junctions, finding that the existence of the junction may nonperturbatively affect the Majorana behavior by introducing spurious non-topological subgap states mimicking zero-modes. We propose a possible solution to this potentially serious problem by showing that junctions made lithographically from two-dimensional (2D) electron gas systems may manifest robust subgap topological properties without any spurious zero modes. We propose a 2D structure that enables multiprobe tunneling experiments providing position-dependent spectroscopy, which can decisively settle outstanding open questions related to the origin of the zero-bias conductance peaks observed experimentally. We also find that junctions with trivial superconductors may result in local perturbations that induce extrinsic low-energy states similar to those associated with wire junctions.

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arXiv2018

Tunneling conductance in semiconductor-superconductor hybrid structures

We study the differential conductance for charge tunneling into a semiconductor wire--superconductor hybrid structure, which is actively investigated as a possible scheme for realizing topological superconductivity and Majorana zero modes. The calculations are done based on a tight-binding model of the heterostructure using both a Blonder-Tinkham-Klapwijk approach and a Keldysh non-equilibrium Green's function method. The dependence of various tunneling conductance features on the coupling strength between the semiconductor and the superconductor, the tunnel barrier height, and temperature is systematically investigated. We find that treating the parent superconductor as an active component of the system, rather than a passive source of Cooper pairs, has qualitative consequences regarding the low-energy behavior of the differential conductance. In particular, the presence of sub-gap states in the parent superconductor, due to disorder and finite magnetic fields, leads to characteristic particle-hole asymmetric features and to the breakdown of the quantization of the zero-bias peak associated with the presence of Majorana zero modes localized at the ends of the wire. The implications of these findings for the effort toward the realization of Majorana bound states with true non-Abelian properties are discussed.

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arXiv2017

Majorana states in prismatic core-shell nanowires

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

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arXiv2017

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

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

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arXiv2017

Proximity-induced low-energy renormalization in hybrid semiconductor-superconductor Majorana structures

A minimal model for the hybrid superconductor-semiconductor nanowire Majorana platform is developed that fully captures the effects of the low-energy renormalization of the nanowire modes arising from the presence of the parent superconductor. In this model, the parent superconductor is an active component that participates explicitly in the low-energy physics, not just a passive partner that only provides proximity-induced Cooper pairs for the nanowire. This treatment on an equal footing of the superconductor and the semiconductor has become necessary in view of recent experiments, which do not allow a consistent interpretation based just on the bare semiconductor properties. The general theory involves the evaluation of the exact semiconductor Green function that includes a dynamical self-energy correction arising from the tunnel-coupled superconductor. General conditions for the emergence of topological superconductivity are worked out for single-band as well as multi-band nanowires and detailed numerical results are given for both infinite and finite wire cases. The topological quantum phase diagrams are provided numerically and the Majorana bound states are obtained along with their oscillatory energy splitting behaviors due to wavefunction overlap in finite wires. Renormalization effects are shown to be both qualitatively and quantitatively important in modifying the low-energy spectrum of the nanowire. The results of the theory are found to be in good qualitative agreement with Majorana nanowire experiments, leading to the conclusion that the proximity-induced low-energy renormalization of the nanowire modes by the parent superconductor is of fundamental importance in superconductor-semiconductor hybrid structures. Implications of the general theory for obtaining true zero energy topological Majorana modes are pointed out.

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arXiv2016

Majorana bound states in non-homogeneous semiconductor nanowires

We demonstrate that partially overlapping Majorana bound states (MBSs) represent a generic low-energy feature that emerges in non-homogeneous semiconductor nanowires coupled to superconductors in the presence of a Zeeman field. The emergence of these low-energy modes is not correlated with any topological quantum phase transition that the system may undergo as the Zeeman field and other control parameters are varied. Increasing the characteristic length scale of the variations in the potential leads to a continuous evolution from strongly overlapping MBSs, which can be viewed as "regular" Andreev bound states (ABSs) that cross zero energy, to well separated weakly overlapping MBSs, which have nearly zero energy in a significant range of parameters and generate signatures similar to the non-degenerate zero-energy Majorana zero modes (MZMs) that emerge in the topological superconducting phase. We show that using charge (or spin) transport measurements it is virtually impossible to distinguish MZMs from weakly overlapping MBSs emerging in the topologically-trivial regime.

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arXiv2016

Experimental Phase Diagram of a One-Dimensional Topological Superconductor

Topological superconductors can host Majorana quasiparticles which supersede the fermion/boson dichotomy and offer a pathway to fault tolerant quantum computation. In one-dimensional systems zero-energy Majorana states are bound to the ends of the topologically superconducting regions. An experimental signature of a Majorana bound state is a conductance peak at zero source-drain voltage bias in a tunneling experiment. Here, we identify the bulk topological phase in a semiconductor nanowire coupled to a conventional superconductor. We map out its phase diagram through the dependence of zero-bias peak on the chemical potential and magnetic field. Our findings are consistent with calculations for a finite-length topological nanowire. Knowledge of the phase diagram makes it possible to predictably tune nanowire segments in and out of the topological phase, thus controlling the positions and couplings of multiple Majorana bound states. This ability is a prerequisite for Majorana braiding, an experiment in which Majorana quantum states are exchanged in order to both demonstrate their non-abelian character and realize topological quantum bits.

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