# Braiding Majorana corner modes in a second-order topological superconductor

## TL;DR

This paper proposes a device using a second-order topological superconductor to host Majorana corner modes, demonstrating their braiding and non-Abelian statistics, advancing potential quantum computing applications.

## Contribution

It introduces a novel device concept for braiding Majorana corner modes in a second-order topological superconductor, including a design for experimental realization.

## Key findings

- Successful braiding of Majorana modes with a non-trivial statistical phase π
- Demonstration of control over Majorana modes via magnetic field rotation and pairing tuning
- Confirmation of Majorana nature through fractional statistics and operator algebra

## Abstract

We propose the concept of a device based on a square-shaped sample of a two-dimensional second-order topological helical superconductor which hosts two zero-dimensional Majorana quasiparticles at the corners. The two zero-energy modes rely on particle-hole symmetry (PHS) and their spacial position can be shifted by rotating an in-plane magnetic field and tuning proximity-induced spin-singlet pairing. We consider an adiabatic cycle performed on the degenerate ground-state manifold and show that it realizes the braiding of the two modes whereby they accumulate a non-trivial statistical phase $\pi$ within one cycle. Alongside with the PHS-ensured operator algebra, the fractional statistics confirms the Majorana nature of the zero-energy excitations. A schematic design for a possible experimental implementation of such a device is presented, which could be a step towards realizing non-Abelian braiding.