Magneto-Josephson effects in junctions with Majorana bound states

TL;DR

This paper explores the duality between particle-hole and spin degrees of freedom in 1D systems with Majorana bound states, revealing novel 4π-periodic magneto-Josephson effects influenced by magnetic field orientation.

Contribution

It uncovers a duality leading to a spin analogue of fractional Josephson effects and demonstrates unconventional 4π-periodic magneto-Josephson phenomena in topological systems.

Findings

Spin current exhibits 4π-periodicity in magnetic field angle.

Josephson current depends periodically on magnetic field orientation.

Duality between particle-hole and spin degrees of freedom is established.

Abstract

We investigate 1D quantum systems that support Majorana bound states at interfaces between topologically distinct regions. In particular, we show that there exists a duality between particle-hole and spin degrees of freedom in certain spin-orbit-coupled 1D platforms such as topological insulator edges. This duality results in a spin analogue of previously explored `fractional Josephson effects'---that is, the spin current flowing across a magnetic junction exhibits 4\pi-periodicity in the relative magnetic field angle across the junction. Furthermore, the interplay between the particle-hole and spin degrees of freedom results in unconventional magneto-Josephson effects, such that the Josephson current is a function of the magnetic field orientation with periodicity 4\pi.