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

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. We develop a general theory to study the effects of random 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 wavefunction component modulus is consistently twice that of the CdGM states. This distinction highlights the uniqueness of MZMs in disordered environments and has significant implications for scanning tunneling microscopy measurements.