# Supercurrent-induced Majorana bound states in a planar geometry

## TL;DR

This paper introduces a novel method for generating Majorana bound states in a 2D electron gas using supercurrents and spin-orbit coupling, highlighting a promising zigzag-shaped junction design.

## Contribution

It proposes a new supercurrent-based approach to induce Majorana states and identifies a zigzag junction as the most feasible configuration.

## Key findings

- Supercurrents can induce Zeeman-like spin splitting with spin-orbit coupling.
- Charge-momentum parity prevents topological gap opening in straight junctions.
- Zigzag-shaped junctions effectively break conservation laws to realize Majorana states.

## Abstract

We propose a new setup for creating Majorana bound states in a two-dimensional electron gas Josephson junction. Our proposal relies exclusively on a supercurrent parallel to the junction as a mechanism of breaking time-reversal symmetry. We show that combined with spin-orbit coupling, supercurrents induce a Zeeman-like spin splitting. Further, we identify a new conserved quantity---charge-momentum parity---that prevents the opening of the topological gap by the supercurrent in a straight Josephson junction. We propose breaking this conservation law by adding a third superconductor, introducing a periodic potential, or making the junction zigzag-shaped. By comparing the topological phase diagrams and practical limitations of these systems we identify the zigzag-shaped junction as the most promising option.