One-dimensional topological superconductivity based entirely on phase control

TL;DR

This paper proposes a method to realize one-dimensional topological superconductivity in planar Josephson junctions solely through phase control, avoiding external magnetic fields, by leveraging phase winding and Fermi velocity differences.

Contribution

It introduces a magnetic-field-free approach to induce topological superconductivity using phase differences and velocity asymmetry in SNS junctions, supported by analytical and numerical analysis.

Findings

Identified parameter regions with topological phases.

Derived critical curves for phase transitions.

Proposed feasible material platforms.

Abstract

Topological superconductivity in one dimension requires time-reversal symmetry breaking, but at the same time it is hindered by external magnetic fields. We offer a general prescription for inducing topological superconductivity in planar superconductor-normal-superconductor-normal-superconductor (SNSNS) Josephson junctions without applying any magnetic fields on the junctions. Our platform relies on two key ingredients: the three parallel superconductors form two SNS junctions with phase winding, and the Fermi velocities for the two spin branches transverse to the junction must be different from one another. The two phase differences between the three superconductors define a parameter plane which includes large topological regions. We analytically derive the critical curves where the topological phase transitions occur, and corroborate the result with a numerical calculation based on a tight-binding model. We further propose material platforms with unequal Fermi velocities, establishing the experimental feasibility of our approach.