Geometric Josephson effects in chiral topological nanowires

TL;DR

This paper explores how geometric and chiral symmetries in topological nanowire Josephson junctions lead to novel effects like a geometrically induced anomalous supercurrent and a curvature-current relation, serving as signatures of topological superconductivity.

Contribution

It introduces the concept of a geometrically induced anomalous Josephson effect and derives a local curvature-current relation in curved topological nanowires.

Findings

Chiral symmetry allows shifting of Andreev spectrum crossings.

Discovery of a geometrically induced anomalous Josephson effect.

Proposed signatures for topological superconductivity in 1D.

Abstract

One of the salient signatures of Majorana zero modes and topological superconductivity is a $4\pi$-periodic Josephson effect due to the combination of fermion parity conservation and the presence of a topologically protected odd number of zero energy crossings in the Andreev spectrum. In this paper, we study this effect in Josephson junctions composed of two semiconducting nanowires with Rashba spin-orbit coupling and induced superconductivity from the proximity effect. For certain orientations of the external magnetic field, such junctions possess a chiral symmetry and we show how this symmetry allows the Andreev spectrum and the protected crossings to be shifted by introducing a relative angle between the two wires. The junction then displays a geometrically induced anomalous Josephson effect, the flow of a supercurrent in the absence of external phase bias. Furthermore, we derive a proportionality relation between the local current density and the local curvature for a single curved wire. This result can be viewed as a one-dimensional analogue of the recently proposed geo-Josephson effect [Kvorning et al., arXiv:1709.00482]. Our two proposed effects can in principle be used as signatures of topological superconductivity in one dimension.