Spontaneous superconducting islands and Hall voltage in clean superconductors

TL;DR

This paper investigates how spontaneous superconducting islands form and influence Hall voltage in clean superconductors using a dissipative Ginzburg--Landau model, revealing complex patterns and sensitivity to initial conditions.

Contribution

It introduces a novel analysis of spontaneous island formation and Hall voltage effects in clean superconductors within a dissipative Ginzburg--Landau framework.

Findings

Superconducting islands form periodic or irregular patterns.

Hall voltage can reverse sign with small initial differences.

Local Hall voltage may persist even when average voltage is zero.

Abstract

We study a clean superconductor in the Hall configuration, in the framework of a purely dissipative time-dependent Ginzburg--Landau theory. We find situations in which the order parameter differs significantly from zero in a set of islands that appear to form a periodic structure. When the pattern of islands becomes irregular, it moves in or against the direction of the current and a Hall voltage is found. Tiny differences in the initial state may reverse the sign of the Hall voltage. When the average Hall voltage vanishes, the local Hall voltage does not necessarily vanish. We examine the influence that several boundary conditions at the electrodes have on these effects.