Coherent Potential Approximation for `d - wave' Superconductivity in Disordered Systems

TL;DR

This paper develops a Coherent Potential Approximation for d-wave superconductivity in disordered systems, reproducing known limits and applying it to compute critical temperatures and density of states, aligning with experimental data.

Contribution

It introduces a CPA formalism for d-wave superconductivity in disordered materials, bridging theoretical models with experimental observations.

Findings

CPA reproduces pair-breaking formulas and self-consistent approximations.

Computed T_c for disordered d-wave systems matches experimental trends.

Density of states analysis explains low-temperature heat capacity behavior.

Abstract

A Coherent Potential Approximation is developed for s-wave and d-wave superconductivity in disordered systems. We show that the CPA formalism reproduces the standard pair-breaking formula, the self-consistent Born Approximation and the self-consistent T-matrix approximation in the appropriate limits. We implement the theory and compute T_c for s-wave and d-wave pairing using an attractive nearest neighbor Hubbard model featuring both binary alloy disorder and a uniform distribution of scattering site potentials. We determine the density of states and examine its consequences for low temperature heat capacity. We find that our results are in qualitative agreement with measurements on Zn doped YBCO superconductors.