Tunable Majorana corner modes in noncentrosymmetric superconductors: Tunneling spectroscopy and edge imperfections

TL;DR

This paper demonstrates how magnetic fields can control Majorana corner modes in noncentrosymmetric superconductors, analyzes the effects of edge imperfections, and proposes tunneling spectroscopy as a method for experimental detection and manipulation.

Contribution

It introduces a method to manipulate Majorana corner modes via magnetic field orientation and studies the impact of edge imperfections on their stability and controllability.

Findings

Majorana corner modes can be controlled by magnetic field direction.

Edge imperfections influence the number and stability of Majorana modes.

Tunneling spectroscopy reveals a periodic conductance pattern related to magnetic field orientation.

Abstract

Majorana corner modes appearing in two-dimensional second-order topological superconductors have great potential applications for fault-tolerant topological quantum computations. We demonstrate that in the presence of an in-plane magentic field two-dimensional ($s+p$)-wave superconductors host Majorana corner modes, whose location can be manipulated by the direction of the magnetic field. In addition, we discuss the effects of edge imperfections on the Majorana corner modes. We describe how different edge shapes and edge disorder affect the number and controllability of the Majorana corner modes, which is of relevance for the implementation of topological quantum computations. We also discuss tunneling spectroscopy in the presence of the Majorana corner modes, where a lead-wire is attached to the corner of the noncentrosymmetric superconductor. The zero-bias differential conductance shows a distinct periodicity with respect to the direction of the magnetic field, which demonstrates the excellent controllability of the Majorana corner modes in this setup. Our results lay down the theoretical groundwork for observing and tuning Majoran corner modes in experiments on ($s+p$)-wave superconductors.