Rotating Majorana Zero Modes in a disk geometry

TL;DR

This paper investigates the manipulation of Majorana zero modes in a p-wave superconductor disk, focusing on their dynamical behavior under magnetic field rotation to enhance topological quantum computing robustness.

Contribution

It provides a detailed analysis of non-adiabatic effects and phase transitions during magnetic field rotation, offering insights into controlling errors in topological quantum computation.

Findings

Oscillations persist even in the adiabatic phase due to frequency-independent coupling.

Controlling rotation frequency can reduce non-adiabatic errors.

Floquet analysis characterizes the phase transition between different dynamical regimes.

Abstract

We study the manipulation of Majorana zero modes in a thin disk made from a $p$-wave superconductor in order to understand their use as a building block for topological quantum computers. We analyze the second-order topological corner modes that arise when an in-plane magnetic field is applied, and calculate their dynamical evolution when rotating the magnetic field, with special emphasis on non-adiabatic effects. We characterize the phase transition between high-frequency and near-adiabatic evolution using Floquet analysis. We show that oscillations persist even in the adiabatic phase because of a frequency independent coupling between zero modes and excited states, which we have quantified numerically and analytically. These results show that controlling the rotation frequency can be a simple method to avoid the non-adiabatic errors originated from this coupling and thus increase the robustness of topological quantum computation.