arXiv subjects

Tudor D. Stanescu

Publications and source records attributed to Tudor D. Stanescu.

At least 55 records · Page 3Linked to original sources

arXiv2016

Spin polarization of Majorana zero modes and topological quantum phase transition in semiconductor Majorana nanowires

A number of recent works have discussed the issue of spin polarization of a Majorana zero mode in condensed matter systems. Here we show that the spin polarization density of a Majorana zero mode, computed as an average of the spin operator over its wave function, vanishes everywhere. A single non-degenerate Majorana zero mode, therefore, does not couple to an applied magnetic field, except via hybridization with higher energy excited states (if present), which may perturb its wave function. If `spin' is defined by considering only the particle components of the wave function, as has been done in some recent works, Majorana zero modes do have a non-zero spatial profile of this quantity, measurable in scanning tunneling microscopy (STM) experiments. However, if such a quantity is measured in spin-resolved tunneling experiments (without spatial resolution), we show that it cannot be used as a unique signature of Majorana zero modes in the topologically non-trivial superconducting phase. As a byproduct, we show that in spatially inhomogeneous systems, accidental zero energy modes, which for all practical purposes behave as Majorana zero modes (including giving rise to a zero bias conductance peak of height 2e^2/h), can appear with increasing magnetic field even in the absence of a topological quantum phase transition (TQPT). But only after gap closing and the associated TQPT, the modes are localized near the system edges, resulting in the maximum topological protection. In the light of these considerations, demonstrating the nonlocal character of the topologically-protected Majorana pair and its emergence {\em after} the systems undergo a TQPT, become critical tasks for the ongoing experimental search for Majorana bound states in condensed matter systems.

cond-mat.mes-hall↗

arXiv2015

Effects of large induced superconducting gap on semiconductor Majorana nanowires

With the recent achievement of extremely high-quality epitaxial interfaces between InAs nanowires and superconducting Al shells with strong superconductor-semiconductor tunnel coupling, a new regime of proximity-induced superconductivity in semiconductors can be explored where the induced gap may be similar in value to the bulk Al gap (large gap) with negligible subgap conductance (hard gap). We propose several experimentally relevant consequences of this large-gap strong-coupling regime for tunneling experiments, and we comment on the prospects of this regime for topological superconductivity. In particular, we show that the advantages of having a strong spin-orbit coupling and a large spin g-factor in the semiconductor nanowire may both be compromised in this strongly coupled limit, and somewhat weaker interface tunneling may be necessary for achieving optimal proximity superconductivity in the semiconductor nanowire. We derive a minimal, generic theory for the strong-coupling hard-gap regime obtaining good qualitative agreement with the experiment and pointing out future directions for further progress toward Majorana nanowires in hybrid semiconductor-superconductor structures.

cond-mat.supr-con↗

arXiv2014

Soft superconducting gap in semiconductor-based Majorana nanowires

We develop a theory for the proximity effect in superconductor-semiconductor-normal metal tunneling structures, which have recently been extensively studied experimentally, leading to the observation of transport signatures consistent with the predicted zero-energy Majorana bound states. We show that our model for the semiconductor nanowire having multiple occupied subbands with different transmission probabilities through the barrier reproduces the observed "soft-gap" behavior associated with substantial subgap tunneling conductance. We study the manifestations of the soft gap phenomenon both in the tunneling conductance and in local density of states measurements and discuss the correlations between these two quantities. We emphasize that the proximity effect associated with the hybridization between low-lying states in the multiband semiconductor and the normal metal states in the lead is an intrinsic effect leading to the soft gap problem. In addition to the intrinsic contribution, there may be extrinsic effects, such as, for example, interface disorder, exacerbating the soft gap problem. Our work establishes the generic possibility of an ubiquitous presence of an intrinsic soft gap in the superconductor-semiconductor-normal metal tunneling transport conductance induced by the inverse proximity effect of the normal metal.

cond-mat.supr-con↗

arXiv2014

Robustness of Topological Superconductivity in Proximity-Coupled Topological Insulator Nanoribbons

We study the low-energy physics of topological insulator (TI) nanoribbons proximity-coupled to s-wave superconductors (SCs) by explicitly incorporating the proximity effects that emerge at the TI-SC interface. We construct a low-energy effective theory that incorporates the proximity effect through an interface contribution containing both normal and anomalous terms and an energy-renormalization matrix. We show that the strength of the proximity-induced gap is determined by the transparency of the interface and the amplitude of the low-energy TI states at the interface. Consequently, the induced gap is strongly band-dependent and collapses for bands containing states with low amplitude at the interface. We find that states with energies within the bulk TI gap have surface-type character and, in the presence of proximity-induced or applied bias potentials, have most of their weight near either the top or the bottom surface of the nanoribbon. As a result, single interface TI-SC structures are susceptible to experiencing a collapse of the induced gap whenever the chemical potential is far enough from the value corresponding to the bulk TI Dirac point and crosses weakly coupled bands. We also find that changing the chemical potential in single-interface structures using gate potentials may be ineffective, as it does not result in a significant increase of the induced gap. On the other hand, we find that symmetric structures, such as a TI nanowire sandwiched between two superconductors, are capable of realizing the full potential of TI-based structures to harbor robust topological superconducting phases.

cond-mat.supr-con↗

arXiv2014

Non-locality of zero-bias anomalies in the topologically-trivial phase of Majorana wires

We show that the topologically trivial zero bias peak (ZBP) emerging in semiconductor Majorana wires due to soft confinement exhibits correlated splitting oscillations as a function of the applied Zeeman field, similar to the correlated splitting of the Majorana ZBP. Also, we find that the presence of a strong impurity can effectively cut the wire in two and destroy the correlated splitting in both the trivial and the Majorana regimes. We identify a strong nonlocal effect that operates only in the topologically trivial regime and demonstrate that the dependence of the ZBP on the confining gate potential at the opposite end in Majorana wires with two normal metal end-contacts represents a powerful tool for discriminating between topologically trivial and nontrivial ZBPs.

cond-mat.mes-hall↗

arXiv2014

Coulomb interaction effects on the Majorana states in quantum wires

The stability of the Majorana modes in the presence of a repulsive interaction is studied in the standard semiconductor wire - metallic superconductor configuration. The effects of short-range Coulomb interaction, which is incorporated using a purely repulsive $δ$-function to model the strong screening effect due to the presence of the superconductor, are determined within a Hartree-Fock approximation of the effective Bogoliubov-De Gennes Hamiltonian that describes the low-energy physics of the wire. Through a numerical diagonalization procedure we obtain interaction corrections to the single particle eigenstates and calculate the extended topological phase diagram in terms of the chemical potential and the Zeeman energy. We find that, for a fixed Zeeman energy, the interaction shifts the phase boundaries to a higher chemical potential, whereas for a fixed chemical potential this shift can occur either to lower or to higher Zeeman energies. This effects can be interpreted as a renormalization of the g-factor due to the interaction. The minimum Zeeman energy needed to realize Majorana fermions decreases with increasing the strength of the Coulomb repulsion. Furthermore, we find that in wires with multi-band occupancy this effect can be enhanced by increasing the chemical potential, i. e. by occupying higher energy bands.

cond-mat.mes-hall↗

arXiv2013

Phase diagram of a three-dimensional antiferromagnet with random magnetic anisotropy

Three-dimensional (3D) antiferromagnets with random magnetic anisotropy (RMA) experimentally studied to date do not have random single-ion anisotropies, but rather have competing two-dimensional and three-dimensional exchange interactions which can obscure the authentic effects of RMA. The magnetic phase diagram Fe$_{x}$Ni$_{1-x}$F$_{2}$ epitaxial thin films with true random single-ion anisotropy was deduced from magnetometry and neutron scattering measurements and analyzed using mean field theory. Regions with uniaxial, oblique and easy plane anisotropies were identified. A RMA-induced glass region was discovered where a Griffiths-like breakdown of long-range spin order occurs.

cond-mat.mtrl-sci↗

arXiv2013

Majorana Fermions in Semiconductor Nanowires: Fundamentals, Modeling, and Experiment

After a recent series of rapid and exciting developments, the long search for the Majorana fermion - the elusive quantum entity at the border between particles and antiparticles - has produced the first positive experimental results, but is not over yet. Originally proposed by E. Majorana in the context of particle physics, Majorana fermions have a condensed matter analog in the zero-energy bound states emerging in topological superconductors. A promising route to engineering topological superconductors capable of hosting Majorana zero modes consists of proximity coupling semiconductor thin films or nanowires with strong spin-orbit interaction to conventional s-wave superconductors in the presence of an external Zeeman field. The Majorana zero mode is predicted to emerge above a certain critical Zeeman field as a zero-energy state localized near the order parameter defects, viz., vortices for thin films and wire-ends for the nanowire. These Majorana bound states are expected to manifest non--Abelian quantum statistics, which makes them ideal building blocks for fault--tolerant topological quantum computation. This review provides an update on current status of the search for Majorana fermions in semiconductor nanowires by focusing on the recent developments, in particular the period following the first reports of experimental signatures consistent with the realization of Majorana bound states in semiconductor nanowire--superconductor hybrid structures. We start with a discussion of the fundamental aspects of the subject, followed by considerations on the realistic modeling which is a critical bridge between theoretical predictions based on idealized conditions and the real world, as probed experimentally. The last part is dedicated to a few intriguing issues that were brought to the fore by the recent encouraging experimental advances.

cond-mat.supr-con↗

arXiv2013

Dimensional crossover in spin-orbit-coupled semiconductor nanowires with induced superconducting pairing

We show that the topological Majorana modes in nanowires much longer than the superconducting coherence length are adiabatically connected with discrete zero-energy states generically occurring in short nanowires. We demonstrate that these zero-energy crossings can be tuned by an external magnetic field and are protected by the particle-hole symmetry. We study the evolution of the low-energy spectrum and the splitting oscillations as a function of magnetic field, wire length, and chemical potential, manifestly establishing that the low-energy physics of short wires is related to that occurring in long wires. This physics, which represents a hallmark of spinless p-wave superconductivity, can be observed in tunneling conductance measurements.

cond-mat.supr-con↗

arXiv2013

Superconducting proximity effect in semiconductor nanowires

We theoretically consider the proximity effect in semiconductor-superconductor hybrid nanostructures, which are being extensively studied in the context of the ongoing search for non-Abelian Majorana fermions in solid state systems. Specifically, we consider the dependence on the thickness of the semiconductor in the direction normal to the interface, a physical effect that has been uncritically neglected in all prior work on the subject. Quite surprisingly, we find the completely unanticipated result that increasing the semiconductor thickness leads to a drastic suppression of the induced superconducting gap due to proximity-induced interband coupling. As a result, in the limit of strong semiconductor-superconductor coupling, the proximity-induced gap becomes much smaller than the bulk superconductor gap and depends weakly on the interface transparency.

cond-mat.mes-hall↗

arXiv2013

To close or not to close: the fate of the superconducting gap across the topological quantum phase transition in Majorana-carrying semiconductor nanowires

We investigate theoretically the low energy physics of semiconductor Majorana wires in the vicinity of a magnetic field-driven topological quantum phase transition (TQPT). The local density of states (LDOS) at the end of the wire, which is directly related to the differential conductance in the limit of point-contact tunneling, is calculated numerically. We find that the dependence of the end-of-wire LDOS on the magnetic field is non-universal and that the signatures associated with the closing of the superconducting gap at the Majorana TQPT are essentially invisible within a significant range of experimentally relevant parameters. Our results provide an explanation for the recent observation of the apparent non-closure of the gap at the Majorana TQPT in semiconductor nanowires.

cond-mat.mes-hall↗

arXiv2012

A Majorana smoking gun for the superconductor-semiconductor hybrid topological system

Recent observations of a zero bias conductance peak in tunneling transport measurements in superconductor--semiconductor nanowire devices provide evidence for the predicted zero--energy Majorana modes, but not the conclusive proof for their existence. We establish that direct observation of a splitting of the zero bias conductance peak can serve as the smoking gun evidence for the existence of the Majorana mode. We show that the splitting has an oscillatory dependence on the Zeeman field (chemical potential) at fixed chemical potential (Zeeman field). By contrast, when the density is constant rather than the chemical potential -- the likely situation in the current experimental set-ups -- the splitting oscillations are generically suppressed. Our theory predicts the conditions under which the splitting oscillations can serve as the smoking gun for the experimental confirmation of the elusive Majorana mode.

cond-mat.mes-hall↗

arXiv2012

Electrostatic effects and band-bending in doped topological insulators

We investigate the electrostatic effects in doped topological insulators by developing a self consistent scheme for an interacting tight binding model. The presence of bulk carriers, in addition to surface electrons, generates an intrinsic inhomogeneous charge density in the vicinity of the surface and, as a result, band bending effects are present. We find that electron doping and hole doping produce band bending effects of similar magnitude and opposite signs. The presence of additional surface dopants breaks this approximate electron-hole symmetry and dramatically affects the magnitude of the band bending. Applying a gate potential can generate a depletion zone characterized by a vanishing carrier density. We find that the density profile in the transition zone between the depleted region and the bulk is independent of the applied potential. In thin films the electrostatic effects are strongly dependent on the carrier charge density. In addition, we find that substrate induced potentials can generate a Rashba type spin-orbit coupling in ultra thin topological insulator films. We calculate the profiles of bulk and surface states in topological insulator films and identify the conditions corresponding to both types of states being localized within the same region in space.

cond-mat.mtrl-sci↗

arXiv2011

Momentum relaxation in a semiconductor proximity-coupled to a disordered s-wave superconductor: effect of scattering on topological superconductivity

We study the superconducting proximity effect between a conventional semiconductor and a disordered s-wave superconductor. We calculate the effective momentum relaxation rate in the semiconductor due to processes involving electron tunneling into a disordered superconductor and scattering off impurities. The magnitude of the effective disorder scattering rate is important for understanding the stability of the topological (chiral p-wave) superconducting state that emerges in the semiconductor, since disorder scattering has a detrimental effect and can drive the system into a non-topological state. We find that the effective impurity scattering rate involves higher-order tunneling processes and is suppressed due to the destructive quantum interference of quasi-particle and quasi-hole trajectories. We show that, despite the fact that both the proximity-induced gap and the effective impurity scattering rate depend on interface transparency, there is a large parameter regime where the topological superconducting phase is robust against disorder in the superconductor. Thus, we establish that the static disorder in the superconductor does not suppress the proximity induced topological superconductivity in the semiconductor.

cond-mat.supr-con↗

arXiv2011

Induced spin texture in semiconductor/topological insulator heterostructures

We show that a semiconductor thin film can acquire a non-trivial spin texture due to the proximity effect induced by a topological insulator. The effect stems from coupling to the topological surface states and is present even when the insulator is doped. We propose a semiconductor/topological insulator heterostructure as a device that allows measuring interface properties and probing surface states in uncompensated samples. We also find that the topological insulator surface modes can be significantly broadened and shifted by the presence of metallic contacts.

cond-mat.mes-hall↗

arXiv2011

Topologically non-trivial superconductivity in spin-orbit coupled systems: Bulk phases and quantum phase transitions

Topologically non-trivial superconductivity has been predicted to occur in superconductors with a sizable spin-orbit coupling in the presence of an external Zeeman splitting. Two such systems have been proposed: (a) s-wave superconductor pair potential is proximity induced on a semiconductor, and (b) pair potential naturally arises from an intrinsic s-wave pairing interaction. As is now well known, such systems in the form of a 2D film or 1D nano-wires in a wire-network can be used for topological quantum computation. When the external Zeeman splitting $Γ$ crosses a critical value $Γ_c$, the system passes from a regular superconducting phase to a non-Abelian topological superconducting phase. In both cases (a) and (b) we consider in this paper the pair potential $Δ$ is strictly s-wave in both the ordinary and the topological superconducting phases, which are separated by a topological quantum critical point at $Γ_c = \sqrt{Δ^2 + μ^2}$, where $μ(>> Δ)$ is the chemical potential. On the other hand, since $Γ_c >> Δ$, the Zeeman splitting required for the topological phase ($Γ> Γ_c$) far exceeds the value ($Γ\sim Δ$) above which an s-wave pair potential is expected to vanish (and the system to become non-superconducting) in the absence of spin-orbit coupling. We are thus led to a situation that the topological superconducting phase appears to set in a parameter regime at which the system actually is non-superconducting in the absence of spin-orbit coupling. In this paper we address the question of how a pure s-wave pair potential can survive a strong Zeeman field to give rise to a topological superconducting phase. We show that the spin-orbit coupling is the crucial parameter for the quantum transition into and the robustness of the topologically non-trivial superconducting phase realized for $Γ>> Δ$.

cond-mat.supr-con↗

arXiv2010

Two-dimensional surface charge transport in topological insulators

We construct a theory of charge transport by the surface states of topological insulators in three dimensions. The focus is on the experimentally relevant case when the electron doping is such that the Fermi energy $ε_F$ and transport scattering time $τ$ satisfy $ε_F τ/\hbar \gg 1$, but sufficiently low that $ε_F$ lies below the bottom of the conduction band. Our theory is based on the spin density matrix and takes the quantum Liouville equation as its starting point. The scattering term is determined accurately to linear order in the impurity density. We consider scattering by charged impurities and short-range scatterers such as surface roughness. We calculate also the polarization function in topological insulators, emphasizing the differences from graphene. We find that the main contribution to the conductivity is $\propto n_i^{-1}$, where $n_i$ is the impurity density, and will have different carrier density dependencies for different forms of scattering. Two different contributions to this conductivity are traced to the scalar and spin-dependent terms in the Hamiltonian and their relative weight depends on the doping density. Our results contain all contributions to the conductivity to orders zero and one in the impurity density. We discuss also a way to determine the dominant scattering angles by studying the ratio of the transport relaxation time to the Bloch lifetime as a function of the Wigner-Seitz radius $r_s$. We also discuss the effect on the surface states of adding metallic contacts.

cond-mat.mes-hall↗

arXiv2010

Topological states in two-dimensional optical lattices

We present a general analysis of two-dimensional optical lattice models that give rise to topologically non-trivial insulating states. We identify the main ingredients of the lattice models that are responsible for the non-trivial topological character and argue that such states can be realized within a large family of realistic optical lattice Hamiltonians with cold atoms. We focus our quantitative analysis on the properties of topological states with broken time-reversal symmetry specific to cold-atom settings. In particular, we analyze finite-size effects, multi-orbital phenomena that give rise to a variety of distinct topological states and transitions between them, the dependence on the trap geometry, and most importantly, the behavior of the edge states for different types of soft and hard boundaries. Furthermore, we demonstrate the possibility of experimentally detecting the topological states through light Bragg scattering of the edge and bulk states.

cond-mat.quant-gas↗