Quantum interference effect on the density of states in disordered d-wave superconductors

TL;DR

This paper investigates how quantum interference affects the quasiparticle density of states in disordered d-wave superconductors, revealing a logarithmic suppression and a resonant peak under certain impurity conditions.

Contribution

It provides a detailed derivation of Goldstone modes and demonstrates the impact of quantum interference on DOS, including a novel delta-function resonance at the unitarity limit.

Findings

Quantum interference causes logarithmic suppression of DOS.

Resonant delta-function peak appears near unitarity and nested Fermi surfaces.

Renormalization factors vary between Born and unitary impurity limits.

Abstract

The quantum interference effect on the quasiparticle density of states (DOS) is studied with the diagrammatic technique in two-dimensional d-wave superconductors with dilute nonmagnetic impurities both near the Born and near the unitary limits. We derive in details the expressions of the Goldstone modes (cooperon and diffuson) for quasiparticle diffusion. The DOS for generic Fermi surfaces is shown to be subject to a quantum interference correction of logarithmic suppression, but with various renormalization factors for the Born and unitary limits. Upon approaching the combined limit of unitarity and nested Fermi surface, the DOS correction is found to become a $\delta$-function of the energy, which can be used to account for the resonant peak found by the numerical studies.