Soliton defects and topological $4\pi$-periodic superconductivity from an orbital magnetic field effect in edge Josephson junctions

TL;DR

This paper demonstrates that an orbital magnetic field effect in edge Josephson junctions of 2D topological insulators can induce topological superconductivity, soliton defects, and Majorana zero modes, with observable $4\pi$-periodic phenomena in magnetic flux and critical current.

Contribution

It introduces a novel mechanism for realizing topological superconductivity via orbital magnetic effects in edge Josephson junctions, revealing soliton defects and Majorana modes with unique flux periodicity.

Findings

Majorana zero modes protected by chiral symmetry.

Magnetic flux induces $2\Phi_0$-spaced oscillations in critical current.

Persistent current with sign reversal in absence of external phase bias.

Abstract

Recently, much research has been dedicated to understanding topological superconductivity and Majorana zero modes induced by a magnetic field in hybrid proximity structures. This paper proposes a realization of topological superconductivity in a short Josephson junction at an edge of a 2D topological insulator subject to a perpendicular magnetic field. The magnetic field effect is entirely orbital, coming from a gradient of the order parameter phase at the edge, which results in a soliton defect at the junction with a pair of gapless Andreev bound states. The latter are reducible to Majorana zero modes by a unitary rotation and protected by a chiral symmetry. Furthermore, both ground state and excitations are quasiperiodic in the magnetic flux enclosed in the junction, with the period equal to the double flux quantum $2\Phi_0 = h/e$. This behaviour follows from the gauge invariance of the $4\pi$ - phase periodicity of the Majorana states and manifests itself as $2\Phi_0$ - spaced magnetic oscillations of the critical current. Another proposed observable is a persistent current occurring in the absence of an external phase bias. Beside the oscillations, it shows a sign reversal prompted by the neutral Majorana zero modes. These findings offer the possibility to access topological superconductivity through low-field dc magnetotransport measurements.