Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields

TL;DR

This paper demonstrates how an in-plane magnetic field can induce and control Majorana corner states in a two-dimensional second-order topological superconductor, enabling tunable localization of these states through magnetic field rotation.

Contribution

It introduces a method to realize and manipulate Majorana corner states in a 2D topological superconductor using magnetic fields, revealing their tunability and potential for quantum applications.

Findings

Magnetic fields induce mass terms leading to Majorana corner states.

Majorana corner states can be moved around by rotating the magnetic field.

The system can host Majorana states at system corners with controllable positions.

Abstract

A two-dimensional second-order topological superconductor exhibits a finite gap in both bulk and edges, with the nontrivial topology manifesting itself through Majorana zero modes localized at the corners, i.e., Majorana corner states. We investigate a time-reversal-invariant topological superconductor in two dimension and demonstrate that an in-plane magnetic field could transform it into a second-order topological superconductor. A detailed analysis reveals that the magnetic field gives rise to mass terms which take distinct values among the edges, and Majorana corner states naturally emerge at the intersection of two adjacent edges with opposite masses. With the rotation of the magnetic field, Majorana corner states localized around the boundary may hop from one corner to a neighboring one and eventually make a full circle around the system when the field rotates by $2\pi$. In the end we briefly discuss physical realizations of this system.