Reentrant topological phase transitions in a disordered spinless superconducting wire

In a one-dimensional spinless p-wave superconductor with coherence length \xi, disorder induces a phase transition between a topologically nontrivial phase and a trivial insulating phase at the critical mean free path l=\xi/2. Here, we show that a multichannel spinless p-wave superconductor goes through an alternation of topologically trivial and nontrivial phases upon increasing the disorder strength, the number of phase transitions being equal to the channel number N. The last phase transition, from a nontrivial phase into the trivial phase, takes place at a mean free path l = \xi/(N+1), parametrically smaller than the critical mean free path in one dimension. Our result is valid in the limit that the wire width W is much smaller than the superconducting coherence length \xi

Effects of electron scattering on the topological properties of nanowires: Majorana fermions from disorder and superlattices

We focus on inducing topological state from regular, or irregular scattering in (i) p-wave superconducting wires and (ii) Rashba wires proximity coupled to an s-wave superconductor. We find that contrary to common expectations the topological properties of both systems are fundamentally different: In p-wave wires, disorder generally has a detrimental effect on the topological order and the topological state is destroyed beyond a critical disorder strength. In contrast, in Rashba wires, which are relevant for recent experiments, disorder can {\it induce} topological order, reducing the need for quasiballistic samples to obtain Majorana fermions. Moreover, we find that the total phase space area of the topological state is conserved for long disordered Rashba wires, and can even be increased in an appropriately engineered superlattice potential.Comment: 5 pages, 3 figs, RevTe

Measurement of spin-dependent conductivities in a two-dimensional electron gas

Spin accumulation is generated by injecting an unpolarized charge current into a channel of GaAs two-dimensional electron gas subject to an in-plane magnetic field, then measured in a non-local geometry. Unlike previous measurements that have used spin-polarized nanostructures, here the spin accumulation arises simply from the difference in bulk conductivities for spin-up and spin-down carriers. Comparison to a diffusive model that includes spin subband splitting in magnetic field suggests a significantly enhanced electron spin susceptibility in the 2D electron gas

Mesoscopic Spin Hall Effect

We investigate the spin Hall effect in ballistic chaotic quantum dots with spin-orbit coupling. We show that a longitudinal charge current can generate a pure transverse spin current. While this transverse spin current is generically nonzero for a fixed sample, we show that when the spin-orbit coupling time is large compared to the mean dwell time inside the dot, it fluctuates universally from sample to sample or upon variation of the chemical potential with a vanishing average. For a fixed sample configuration, the transverse spin current has a finite typical value ~e^2 V/h, proportional to the longitudinal bias V on the sample, and corresponding to about one excess open channel for one of the two spin species. Our analytical results are in agreement with numerical results in a diffusive system [W. Ren et al., Phys. Rev. Lett. 97, 066603 (2006)] and are further confirmed by numerical simulation in a chaotic cavity.Comment: 4 pages, 2 figure

Supersymmetry in the Majorana Cooper-Pair Box

Over the years, supersymmetric quantum mechanics has evolved from a toy model of high energy physics to a field of its own. Although various examples of supersymmetric quantum mechanics have been found, systems that have a natural realization are scarce. Here, we show that the extension of the conventional Cooper-pair box by a 4pi-periodic Majorana-Josephson coupling realizes supersymmetry for certain values of the ratio between the conventional Josephson and the Majorana- Josephson coupling strength. The supersymmetry we find is a "hidden" minimally bosonized supersymmetry that provides a non-trivial generalization of the supersymmetry of the free particle and relies crucially on the presence of an anomalous Josephson junction in the system. We show that the resulting degeneracy of the energy levels can be probed directly in a tunneling experiment and discuss the various transport signatures. An observation of the predicted level degeneracy would provide clear evidence for the presence of the anomalous Josephson coupling.Comment: 10 pages, 5 figure

Chirality blockade of Andreev reflection in a magnetic Weyl semimetal

A Weyl semimetal with broken time-reversal symmetry has a minimum of two species of Weyl fermions, distinguished by their opposite chirality, in a pair of Weyl cones at opposite momenta $\pm K$ that are displaced in the direction of the magnetization. Andreev reflection at the interface between a Weyl semimetal in the normal state (N) and a superconductor (S) that pairs $\pm K$ must involve a switch of chirality, otherwise it is blocked. We show that this "chirality blockade" suppresses the superconducting proximity effect when the magnetization lies in the plane of the NS interface. A Zeeman field at the interface can provide the necessary chirality switch and activate Andreev reflection.Comment: 15 pages, 9 figures. V2: added investigation of the dependence of the chirality blockade on the direction of the magnetization and (Appendix C) calculations of the Fermi-arc mediated Josephson effec

Quantal Andreev billiards: Semiclassical approach to mesoscale oscillations in the density of states

Andreev billiards are finite, arbitrarily-shaped, normal-state regions, surrounded by superconductor. At energies below the superconducting gap, single-quasiparticle excitations are confined to the normal region and its vicinity, the essential mechanism for this confinement being Andreev reflection. This Paper develops and implements a theoretical framework for the investigation of the short-wave quantal properties of these single-quasiparticle excitations. The focus is primarily on the relationship between the quasiparticle energy eigenvalue spectrum and the geometrical shape of the normal-state region, i.e., the question of spectral geometry in the novel setting of excitations confined by a superconducting pair-potential. Among the central results of this investigation are two semiclassical trace formulas for the density of states. The first, a lower-resolution formula, corresponds to the well-known quasiclassical approximation, conventionally invoked in settings involving superconductivity. The second, a higher-resolution formula, allows the density of states to be expressed in terms of: (i) An explicit formula for the level density, valid in the short-wave limit, for billiards of arbitrary shape and dimensionality. This level density depends on the billiard shape only through the set of stationary-length chords of the billiard and the curvature of the boundary at the endpoints of these chords; and (ii) Higher-resolution corrections to the level density, expressed as a sum over periodic orbits that creep around the billiard boundary. Owing to the fact that these creeping orbits are much longer than the stationary chords, one can, inter alia, hear the stationary chords of Andreev billiards.Comment: 52 pages, 15 figures, 1 table, RevTe

Topologically Protected Loop Flows in High Voltage AC Power Grids

Geographical features such as mountain ranges or big lakes and inland seas often result in large closed loops in high voltage AC power grids. Sizable circulating power flows have been recorded around such loops, which take up transmission line capacity and dissipate but do not deliver electric power. Power flows in high voltage AC transmission grids are dominantly governed by voltage angle differences between connected buses, much in the same way as Josephson currents depend on phase differences between tunnel-coupled superconductors. From this previously overlooked similarity we argue here that circulating power flows in AC power grids are analogous to supercurrents flowing in superconducting rings and in rings of Josephson junctions. We investigate how circulating power flows can be created and how they behave in the presence of ohmic dissipation. We show how changing operating conditions may generate them, how significantly more power is ohmically dissipated in their presence and how they are topologically protected, even in the presence of dissipation, so that they persist when operating conditions are returned to their original values. We identify three mechanisms for creating circulating power flows, (i) by loss of stability of the equilibrium state carrying no circulating loop flow, (ii) by tripping of a line traversing a large loop in the network and (iii) by reclosing a loop that tripped or was open earlier. Because voltage angles are uniquely defined, circulating power flows can take on only discrete values, much in the same way as circulation around vortices is quantized in superfluids.Comment: 12 pages 6 figures + Supplementary Material, Accepted for publication in New Journal of Physic