Quasiclassical theory of disordered Rashba superconductors

We derive the quasiclassical equations that describe two-dimensional superconductors with a large Rashba spin-orbit coupling and in the presence of impurities. These equations account for the helical phase induced by an in-plane magnetic field, with a superconducting order parameter that is spatially modulated along a direction perpendicular to the field. We also derive the generalized Ginzburg-Landau functional, which includes a linear-in-gradient term corresponding to the helical phase. This theory paves the way for studies of the proximity effect in two-dimensional electron gases with large spin-orbit coupling.Comment: 6 pages, 1 figur

Topological Josephson ϕ0{\phi}_0-junctions

We study the effect of a magnetic field on the current-phase relation of a topological Josephson junction formed by connecting two superconductors through the helical edge states of a quantum spin-Hall insulator. We predict that the Zeeman effect along the spin quantization axis of the helical edges results in an anomalous Josephson relation that allows for a supercurrent to flow in the absence of superconducting phase bias. We relate the associated field-tunable phase shift $\phi_0$ in the Josephson relation of such a $\phi_0$-junction to the existence of a so-called helical superconductivity, which may result from the interplay of the Zeeman effect and spin-orbit coupling. We analyze the dependence of the magneto-supercurrent on the junction length and discuss its observability in suitably designed hybrid structures subject to an in-plane magnetic field.Comment: 7 pages, 3 figures, Appendix and references adde

Non-equilibrium Josephson effect through helical edge states

We study Josephson junctions between superconductors connected through the helical edge states of a two-dimensional topological insulator in the presence of a magnetic barrier. As the equilibrium Andreev bound states of the junction are 4Pi-periodic in the superconducting phase difference, it was speculated that, at finite dc bias voltage, the junction exhibits a fractional Josephson effect with half the Josephson frequency. Using the scattering matrix formalism, we show that signatures of this effect can be seen in the finite-frequency current noise. Furthermore, we discuss other manifestations of the Majorana bound states forming at the edges of the superconductors.Comment: 4+ pages, 3 figure

Anomalous Josephson effect in semiconducting nanowires as a signature of the topologically nontrivial phase

We study Josephson junctions made of semiconducting nanowires with Rashba spin-orbit coupling, where superconducting correlations are induced by the proximity effect. In the presence of a suitably directed magnetic field, the system displays the anomalous Josephson effect: a nonzero supercurrent in the absence of a phase bias between two superconductors. We show that this anomalous current can be increased significantly by tuning the nanowire into the helical regime. In particular, in a short junction, a large anomalous current is a signature for topologically nontrivial superconductivity in the nanowire.Comment: 10 pages, 9 figures; published versio

How many quasiparticles can be in a superconductor?

Experimentally and mysteriously, the concentration of quasiparticles in a gapped superconductor at low temperatures always by far exceeds its equilibrium value. We study the dynamics of localized quasiparticles in superconductors with a spatially fluctuating gap edge. The competition between phonon-induced quasiparticle recombination and generation by a weak non-equilibrium agent results in an upper bound for the concentration that explains the mystery.Comment: 8 pages, 8 figure

Ac Josephson Effect in Topological Josephson Junctions

Topological superconductors admit zero-energy Majorana bound states at their boundaries. In this review article, we discuss how to probe these Majorana bound states in Josephson junctions between two topological superconductors. In the absence of an applied bias, the presence of these states gives rise to an Andreev bound state whose energy varies $4\pi$-periodically in the superconducting phase difference. An applied voltage bias leads to a dynamically varying phase according to the Josephson relation. Furthermore, it leads to dynamics of the occupation of the bound state via its non-adiabatic coupling to the continuum. While the Josephson relation suggests a fractional Josephson effect due to the $4\pi$-periodicity of the bound state, its observability relies on the conservation of the occupation of the bound state on the experimentally probed time scale. We study the lifetime of the bound state and identify the time scales it has to be compared to. In particular, we are interested in signatures of the fractional Josephson effect in the Shapiro steps and in current noise measurements. We also discuss manifestations of the zero-energy Majorana states on the dissipative subgap current.Comment: 19 pages, 12 figure

Disordered topological metals

Topological behavior can be masked when disorder is present. A topological insulator, either intrinsic or interaction induced, may turn gapless when sufficiently disordered. Nevertheless, the metallic phase that emerges once a topological gap closes retains several topological characteristics. By considering the self-consistent disorder-averaged Green function of a topological insulator, we derive the condition for gaplessness. We show that the edge states survive in the gapless phase as edge resonances and that, similar to a doped topological insulator, the disordered topological metal also has a finite, but nonquantized topological index. We then consider the disordered Mott topological insulator. We show that within mean-field theory, the disordered Mott topological insulator admits a phase where the symmetry-breaking order parameter remains nonzero but the gap is closed, in complete analogy to “gapless superconductivity” due to magnetic disorder