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

Thermodynamics of Coherent Structures near Phase Transitions

Phase transitions within large-scale systems may be modeled by using partial differential equations, in which system dynamics are captured by appropriate polynomial potentials. The ability to simulate and predict phase transition behavior has many applications, from material behaviors (e.g., liquid crystal phase transformations, coherent movement of granular materials) to traffic congestion. Coherent structures in these systems evolve along a single spatial dimension randomly through time; thus, the statistical behavior of these fields is of greater interest than particular system results. Past research focused on deriving solutions to the system probability density function (PDF) and verifying solutions for fourth-order and other simple potentials. Until recently, the extent to which these solutions could be verified was limited by computing power. This work focused on verifying solutions for PDFs of sixth-order and tenth-order potentials, which describe more complex phase transition behaviors, and determining their respective correlation functions. Large-scale MATLAB simulations were used to model the evolution of fields at certain system “temperatures”, for which statistical PDFs and correlation functions were computed. Once fully validated, this approach will enable a better understanding of successive phase transitions in complex materials, and allow for accurate modeling of these system behaviors based on material properties. In the future it would be beneficial to evaluate the field dynamics of higher-order potentials at a smaller scale to gain further insight on the behavior of stochastic processes in large-scale systems