# Flux-induced Topological Superconductor in Planar Josephson Junction

## TL;DR

This paper proposes a flux-tunable planar Josephson junction device that can host and manipulate Majorana zero-modes, enabling topological quantum computing applications with controllable phase differences and network configurations.

## Contribution

It introduces a novel flux-induced topological superconductor in a planar Josephson junction, allowing easy tuning between trivial and non-trivial phases and proposing a braiding scheme for Majorana modes.

## Key findings

- Magnetic flux induces topologically non-trivial phases in the junction.
- Majorana zero-modes can be formed and manipulated at the nanowire ends.
- The device can be integrated into 2D networks for quantum computing.

## Abstract

A planar Josephson junction with a normal metal attached on its top surface will form a hollow nanowire structure due to its three dimensional nature. In such hollow nanowire structure, the magnetic flux induced by a small magnetic field (about 0.01T) will tune the system into topologically non-trivial phase and therefore two Majorana zero-modes will form at the ends of the nanowire. Through tuning the chemical potential of the normal metal, the topologically non-trivial phase can be obtained for almost all energy within the band. Furthermore, the system can be conveniently tuned between the topologically trivial and non-trivial phases via the phase difference between the superconductors. Such device, manipulable through flux, can be conveniently fabricated into desired 2D networks. Finally, we also propose a cross-shaped junction realizing the braiding of Majorana zero-modes through manipulating the phase differences.