Tunable $\varphi$-Josephson junction with a quantum anomalous Hall insulator

TL;DR

This paper theoretically demonstrates a tunable $$-Josephson junction using a quantum anomalous Hall insulator, where an in-plane Zeeman field induces a controllable phase shift in the supercurrent due to symmetry properties.

Contribution

It introduces a novel tunable $$-junction mechanism leveraging the symmetry of quantum anomalous Hall insulators and Zeeman fields, with a detailed phenomenological explanation.

Findings

Zeeman fields induce a phase shift $$ in the Josephson current.

The phase shift depends on the Zeeman field amplitude and direction.

The symmetry analysis explains the physical origin of the $$-phase shift.

Abstract

We theoretically study the Josephson current in a superconductor/quantum anomalous Hall insulator/superconductor junction by using the lattice Green function technique. When an in-plane external Zeeman field is applied to the quantum anomalous Hall insulator, the Josephson current $J$ flows without a phase difference across the junction $\theta$. The phase shift $\varphi$ appealing in the current-phase relationship $J\propto \sin(\theta-\varphi$) is proportional to the amplitude of Zeeman fields and depends on the direction of Zeeman fields. A phenomenological analysis of the Andreev reflection processes explains the physical origin of $\varphi$. A quantum anomalous Hall insulator breaks time-reversal symmetry and mirror reflection symmetry simultaneously. However it preserves magnetic mirror reflection symmetry. Such characteristic symmetry property enable us to have a tunable $\varphi$-junction with a quantum Hall insulator.