Statistical Signatures of Majorana Zero Modes in Disordered Topological Superconductor Antidot Vortices

TL;DR

This paper develops a theory to distinguish Majorana zero modes from Caroli-de Gennes-Matricon states in disordered topological superconductor vortices, using statistical signatures measurable by scanning tunneling microscopy.

Contribution

It introduces a statistical approach combining analytical and numerical methods to identify unique signatures of Majorana zero modes amidst disorder.

Findings

Variance of MZM probability density is twice that of CdGM states.

Real wave functions of MZMs lead to distinct statistical signatures.

Measurable differences can be detected via scanning tunneling microscopy.

Abstract

An antidot-pinned vortex in a three-dimensional topological insulator-superconductor platform hosts a Majorana zero mode (MZM). However, numerous Caroli-de Gennes-Matricon (CdGM) states coexist with it. We develop a general theory to study the effects of disorder on the system, emphasizing the difference between Majorana zero mode and CdGM states. Using both an analytical random matrix theory approach and numerical simulations, we derive the statistical distributions of these states. Our results demonstrate that the variance of the MZM probability density is twice that of the CdGM states, a difference due to the former having a real wave function as opposed to a complex one. This distinction can be measured by using scanning tunneling microscopy in a disordered antidot vortex, providing a signature of MZM beyond the zero-bias conductance peak.