Evolution of the Density of States Gap in a Disordered Superconductor

TL;DR

This paper investigates how disorder affects the density of states gap in a superconductor, revealing a transition from a gapped to a pseudo-gap state and identifying a crossover between Fermi- and Bose-insulators.

Contribution

First computation of the density of states in a finite-dimensional disordered fermion model using Quantum Monte Carlo and maximum entropy methods.

Findings

Disorder closes the gap at weak coupling with the destruction of superconductivity.

A pseudo-gap persists beyond the loss of long-range order at intermediate coupling.

The results indicate a crossover between Fermi- and Bose-insulators.

Abstract

It has only recently been possible to study the superconducting state in the attractive Hubbard Hamiltonian via a direct observation of the formation of a gap in the density of states N(w). Here we determine the effect of random chemical potentials on N(w) and show that at weak coupling, disorder closes the gap concurrently with the destruction of superconductivity. At larger, but still intermediate coupling, a pseudo-gap in N(w) remains even well beyond the point at which off-diagonal long range order vanishes. This change in the elementary excitations of the insulating phase corresponds to a crossover between Fermi- and Bose-Insulators. These calculations represent the first computation of the density of states in a finite dimensional disordered fermion model via the Quantum Monte Carlo and maximum entropy methods.