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.Comment: 8 pages, 5 figures; published versio

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.Comment: 29 pages, 34 figures (references and new section added; published version

Search for Majorana fermions in multiband semiconducting nanowires

We study multiband semiconducting nanowires proximity-coupled with an s-wave superconductor. We show that when odd number of subbands are occupied the system realizes non-trivial topological state supporting Majorana modes localized at the ends. We study the topological quantum phase transition in this system and analytically calculate the phase diagram as a function of the chemical potential and magnetic field. Our key finding is that multiband occupancy not only lifts the stringent constraint of one-dimensionality but also allows to have higher carrier density in the nanowire and as such multisubband nanowires are better-suited for observing the Majorana particle. We study the robustness of the topological phase by including the effects of the short- and long-range disorder. We show that in the limit of strong interband mixing there is an optimal regime in the phase diagram ("sweet spot") where the topological state is to a large extent insensitive to the presence of disorder.Comment: 4 pages, 3 figures, expanded version includes new results; accepted for publication in PR

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.Comment: published version, 7 pages, 7 color figure

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.Comment: published version, 11+ pages, 8 figure

Nearest-neighbour Attraction Stabilizes Staggered Currents in the 2D Hubbard Model

Using a strong-coupling approach, we show that staggered current vorticity does not obtain in the repulsive 2D Hubbard model for large on-site Coulomb interactions, as in the case of the copper oxide superconductors. This trend also persists even when nearest-neighbour repulsions are present. However, staggered flux ordering emerges {\bf only} when attractive nearest-neighbour Coulomb interactions are included. Such ordering opens a gap along the $(\pi,0)-(0,\pi)$ direction and persists over a reasonable range of doping.Comment: 5 pages with 5 .eps files (Typos in text are corrected