Magnetic anisotropy of critical current in nanowire Josephson junction with spin-orbit interaction

We develop and study theoretically a minimal model of semiconductor nanowire Josephson junction that incorporates Zeeman and spin-orbit effects. The DC Josephson current is evaluated from the phase-dependent energies of Andreev levels. Upon changing the magnetic field applied, the critical current oscillates manifesting cusps that signal the $0$-$\pi$ transition. Without spin-orbit interaction, the oscillations and positions of cusps are regular and do not depend on the direction of magnetic field. In the presence of spin-orbit interaction, the magnetic field dependence of the current becomes anisotropic and irregular. We investigate this dependence in detail and show that it may be used to characterize the strength and direction of spin-orbit interaction in experiments with nanowires.Comment: submitted to EPL. The manuscript has a supplementary note. 5 page with 4 figures + 2 pages with 2 figure

Critical current oscillation by magnetic field in semiconductor nanowire Josephson junction

We study theoretically the critical current in semiconductor nanowire Josephson junction with strong spin-orbit interaction. The critical current oscillates by an external magnetic field. We reveal that the oscillation of critical current depends on the orientation of magnetic field in the presence of spin-orbit interaction. We perform a numerical simulation for the nanowire by using a tight-binding model. The Andreev levels are calculated as a function of phase difference $\varphi$ between two superconductors. The DC Josephson current is evaluated from the Andreev levels in the case of short junctions. The spin-orbit interaction induces the effective magnetic field. When the external field is parallel with the effective one, the critical current oscillates accompanying the $0$-$\pi$ like transition. The period of oscillation is longer as the angle between the external and effective fields is larger

Josephson and proximity effects on the surface of a topological insulator

We investigate Josephson and proximity effects on the surface of a topological insulator on which superconductors and a ferromagnet are deposited. The superconducting regions are described by the conventional BCS Hamiltonian, rather than the superconducting Dirac Hamiltonian. Junction interfaces are assumed to be dirty. We obtain analytical expressions of the Josephson current and the proximity-induced anomalous Green's function on the topological insulator. The dependence of the Josephson effect on the junction length, the temperature, the chemical potential and the magnetization is discussed. It is also shown that the proximity-induced pairing on the surface of a topological insulator includes even and odd frequency triplet pairings as well as a conventional s-wave one.Comment: 7 pages, 5 figure

Metric perturbation from inflationary magnetic field and generic bound on inflation models

There is an observational indication of extragalactic magnetic fields. No known astrophysical process can explain the origin of such large scale magnetic fields, which motivates us to look for their origin in primordial inflation. By solving the linearized Einstein equations, we study metric perturbations sourced by magnetic fields that are produced during inflation. This leads to a simple but robust bound on the inflation models by requiring that the induced metric perturbation should not exceed the observed value 10^-5. In case of the standard single field inflation model, the bound can be converted into a lower bound on the Hubble parameter during inflation.Comment: 14 page

Order, disorder and tunable gaps in the spectrum of Andreev bound states in a multi-terminal superconducting device

We consider the spectrum of Andreev bound states (ABSs) in an exemplary 4-terminal superconducting structure where 4 chaotic cavities are connected by QPCs to the terminals and to each other forming a ring. Such a tunable device can be realized in 2DEG-superconductor structures. We concentrate on the limit of a short structure and large conductance of the QPCs where a quasi-continuous spectrum is formed. The energies can be tuned by the superconducting phases. We observe the opening and closing of gaps in the spectrum. This concerns the usual proximity gap that separates the levels from zero energy as well as less usual "smile" gaps that split the levels of the spectrum. We demonstrate a remarkable crossover in the overall spectrum that occurs upon changing the ratio of conductance of the inner and outer QPCs. At big values of the ratio, the levels exhibit a generic behavior expected for the spectrum of a disordered system manifesting level repulsion and "Brownian motion" upon changing the phases. At small values of the ratio, the levels are squeezed into narrow bunches separated by wide smile gaps. Each bunch consists of almost degenerate ABSs. We study in detail the properties of the spectrum in the limit of a small ratio, paying special attention to the crossings of bunches. We distinguish two types of crossings: i. with a regular phase dependence of the levels and ii. crossings where the Brownian motion of the levels leads to an apparently irregular phase-dependence. We work out a perturbation theory to explain the observations. The unusual properties of the spectrum originate from unobvious topological effects. Topology of the first kind is related to the winding of the semiclassical Green's function. It is responsible for the proximity gaps. Topology of the second kind comes about the discreteness of the number of modes and is responsible for the smile gaps.Comment: 20 pages with 20 figure