Theory of reentrant superconductivity in Corbino Josephson junctions

TL;DR

This paper investigates reentrant superconductivity in Corbino Josephson junctions, revealing topological effects that could help identify topological superconductivity through flux periodicity changes.

Contribution

It introduces a simple analytical model showing reentrant superconductivity with a period related to junction geometry, and finds a halving of this period in topological cases.

Findings

Circular junctions show similar behavior regardless of topology.

Non-circular junctions exhibit reentrant superconductivity.

Topological case shows halved flux period in non-circular junctions.

Abstract

Josephson junctions made of conventional superconductors display Fraunhofer-like oscillations of the critical current as a function of the threaded magnetic flux. When the superconductors are deposited on the surface of a three-dimensional topological insulator, this pattern is slightly modified due to the presence of chiral Majorana modes. Here we calculate the critical current of a Corbino Josephson junction, where the fluxoid becomes quantized and the superconducting phase has an integer winding. We discover that circular junctions exhibit similar behavior in both topologically trivial and non-trivial scenarios, while non-circular junctions demonstrate a remarkable distinction. Using a simple analytical model, we show that these non-circular junctions exhibit reentrant superconductivity with a period related to their number of corners, and numerically we find that this period is halved in the topological case. The period halving may help establish the existence of topological superconductivity in hybrid topological insulator-superconductor junctions.