# Majorana Zero-Modes in a Two-Dimensional $p$-Wave Superconductor

## TL;DR

This paper investigates the emergence and manipulation of Majorana zero-modes at the edges of a two-dimensional topological superconductor, focusing on a triplet phase in doped Bi$_2$Se$_3$ and their potential use in quantum computing.

## Contribution

It demonstrates how in-plane magnetic fields can create and control Majorana modes in a 2D topological superconductor, proposing new methods for their braiding.

## Key findings

- Magnetic field opens a gap in surface modes, inducing Majorana zero-modes.
- Majorana modes can be manipulated by changing the magnetic field orientation.
- Potential applications in topological quantum computation.

## Abstract

We analyze the formation of Majorana zero-modes at the edge of a two-dimensional topological superconductor. In particular, we study a time-reversal-invariant triplet phase that is likely to exist in doped Bi$_2$Se$_3$. Upon the introduction of an in-plane magnetic field to the superconductor, a gap is opened in the surface modes, which induces localized Majorana modes. The position of these modes can be simply manipulated by changing the orientation of the applied field, yielding novel methods for braiding these states with possible applications to topological quantum computation.