Anisotropic topological superconductivity in Josephson junctions

TL;DR

This paper explores how magnetic and crystalline anisotropies influence topological superconductivity in Josephson junctions, revealing conditions for tuning into topological states through magnetic field orientation and SOC interplay.

Contribution

It provides a detailed analysis of anisotropic effects on topological phases in Josephson junctions, including the impact of Rashba and Dresselhaus SOCs and magnetic field orientation.

Findings

Topological phase diagram depends on magnetic field and crystallographic orientation when both SOCs coexist.

Anisotropic current-phase relation can reveal the ground-state phase in phase-unbiased junctions.

Proper balancing of magnetic field, SOCs, and orientation enables topological superconductivity with a sizable gap.

Abstract

We investigate the effects of magnetic and crystalline anisotropies on the topological superconducting state of planar Josephson junctions (JJs). In junctions where only Rashba spin-orbit coupling (SOC) is present, the topological phase diagram is insensitive to the supercurrent direction, but exhibits a strong dependence on the magnetic field orientation. However, when both Rashba and Dresselhaus SOCs coexist, the topological phase diagram strongly depends on both the magnetic field and junction crystallographic orientations. We examine the impact of the magnetic and crystalline anisotropy on the current-phase relation (CPR), energy spectrum, and topological gap of phase-biased JJs, where the junction is connected in a loop and the superconducting phase difference is fixed by a loop-threading magnetic flux. The anisotropic CPR can be used to extract the ground-sate phase (i.e. the superconducting phase difference that minimizes the system free energy) behavior in phase-unbiased JJs with no magnetic flux. Under appropriate conditions, phase-unbiased JJs can self-tune into or out of the topological superconducting state by rotating the in-plane magnetic field. The magnetic field orientations at which topological transitions occur strongly depend on both the junction crystallographic orientation and the relative strength between Rashba and Dresselhaus SOCs. We find that for an optimal practical application, in which the junction exhibits topological superconductivity with a sizable topological gap, a careful balancing of the magnetic field direction, the junction crystallographic orientation, and the relative strengths of the Rashba and Dresselhaus SOCs is required. We discuss the considerations that must be undertaken to achieve this balancing for various junction types and parameters.