Topological Josephson ${\phi}_0$-junctions

TL;DR

This paper predicts a magnetic-field-induced anomalous supercurrent in topological Josephson junctions, revealing a tunable phase shift due to helical superconductivity, with potential for experimental observation in hybrid structures.

Contribution

It introduces the concept of a $$-junction with a field-tunable phase shift caused by Zeeman effect and spin-orbit coupling in topological superconductors.

Findings

Zeeman effect induces anomalous Josephson relation.

Supercurrent can flow without phase bias.

Dependence of magneto-supercurrent on junction length.

Abstract

We study the effect of a magnetic field on the current-phase relation of a topological Josephson junction formed by connecting two superconductors through the helical edge states of a quantum spin-Hall insulator. We predict that the Zeeman effect along the spin quantization axis of the helical edges results in an anomalous Josephson relation that allows for a supercurrent to flow in the absence of superconducting phase bias. We relate the associated field-tunable phase shift $\phi_0$ in the Josephson relation of such a $\phi_0$-junction to the existence of a so-called helical superconductivity, which may result from the interplay of the Zeeman effect and spin-orbit coupling. We analyze the dependence of the magneto-supercurrent on the junction length and discuss its observability in suitably designed hybrid structures subject to an in-plane magnetic field.