Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class D thermal quantum Hall effect

TL;DR

This study numerically examines the quasiparticle density of states in a two-dimensional disordered superconductor, revealing distinct behaviors across metallic, insulating, and critical phases in the class D thermal quantum Hall effect.

Contribution

It provides a detailed numerical analysis of the density of states in class D systems, confirming theoretical predictions and exploring phase transitions.

Findings

Logarithmic divergence of $ ho(E)$ in the thermal metal phase.

Finite $ ho(E)$ at $E=0$ in insulator and quantized Hall phases.

$ ho(E)$ decreases as $|E|$ approaches zero at the transition, following a $|E| ext{ln}(1/|E|)$ behavior.

Abstract

We investigate numerically the quasiparticle density of states $\varrho(E)$ for a two-dimensional, disordered superconductor in which both time-reversal and spin-rotation symmetry are broken. As a generic single-particle description of this class of systems (symmetry class D), we use the Cho-Fisher version of the network model. This has three phases: a thermal insulator, a thermal metal, and a quantized thermal Hall conductor. In the thermal metal we find a logarithmic divergence in $\varrho(E)$ as $E\to 0$, as predicted from sigma model calculations. Finite size effects lead to superimposed oscillations, as expected from random matrix theory. In the thermal insulator and quantized thermal Hall conductor, we find that $\varrho(E)$ is finite at E=0. At the plateau transition between these phases, $\varrho(E)$ decreases towards zero as $|E|$ is reduced, in line with the result $\varrho(E) \sim |E|\ln(1/|E|)$ derived from calculations for Dirac fermions with random mass.