Density of states at disorder-induced phase transitions in a multichannel Majorana wire

TL;DR

This paper investigates the density of states at disorder-induced topological phase transitions in multichannel Majorana wires, revealing Dyson and power-law singularities and linking critical exponents to transport properties.

Contribution

It demonstrates the nature of density of states singularities at phase transitions and relates critical exponents to transport parameters using superuniversality.

Findings

Dyson singularity at topological transitions

Power-law singularity away from critical points

Relation of critical exponent to mean free path and coherence length

Abstract

An $N$-channel spinless p-wave superconducting wire is known to go through a series of $N$ topological phase transitions upon increasing the disorder strength. Here, we show that at each of those transitions the density of states shows a Dyson singularity $\nu(\varepsilon) \propto \varepsilon^{-1}|\ln\varepsilon|^{-3} $, whereas $\nu(\varepsilon) \propto \varepsilon^{|\alpha|-1}$ has a power-law singularity for small energies $\varepsilon$ away from the critical points. Using the concept of "superuniversality" [Gruzberg, Read, and Vishveshwara, Phys. Rev. B 71, 245124 (2005)], we are able to relate the exponent $\alpha$ to the wire's transport properties at zero energy and, hence, to the mean free path $l$ and the superconducting coherence length $\xi$.