Random-matrix theory of Majorana fermions and topological superconductors

TL;DR

This paper applies random-matrix theory to analyze Majorana fermions and topological superconductors, providing insights into their spectral properties, symmetries, and transport phenomena across various experimental platforms.

Contribution

It introduces a comprehensive RMT framework for topological superconductors, encompassing spectral, scattering, and transport properties, highlighting new universal features and symmetry classifications.

Findings

Spectral peak and level repulsion in Hamiltonian ensembles

Universal conductance and shot noise signatures of Majorana modes

Topological phase transitions characterized by RMT statistics

Abstract

I. Introduction (What is new in RMT, Superconducting quasiparticles, Experimental platforms) II. Topological superconductivity (Kitaev chain, Majorana operators, Majorana zero-modes, Phase transition beyond mean-field) III. Fundamental symmetries (Particle-hole symmetry, Majorana representation, Time-reversal and chiral symmetry) IV. Hamiltonian ensembles (The ten-fold way, Midgap spectral peak, Energy level repulsion) V. Scattering matrix ensembles (Fundamental symmetries, Chaotic scattering, Circular ensembles, Topological quantum numbers) VI. Electrical conduction (Majorana nanowire, Counting Majorana zero-modes, Conductance distribution, Weak antilocalization, Andreev resonances, Shot noise of Majorana edge modes) VII. Thermal conduction (Topological phase transitions, Super-universality, Heat transport by Majorana edge modes, Thermopower and time-delay matrix, Andreev billiard with chiral symmetry) VIII. Josephson junctions (Fermion parity switches, 4{\pi}-periodic Josephson effect, Discrete vortices) IX. Conclusion