Pauli-limited upper critical field in dirty d-wave superconductors

TL;DR

This paper investigates how impurity scattering affects the upper critical field and FFLO phase stability in dirty d-wave superconductors, revealing that the FFLO state remains robust despite disorder.

Contribution

It provides a detailed theoretical analysis of impurity effects on the phase diagram and FFLO stability in dirty d-wave superconductors using quasiclassical methods.

Findings

FFLO phase survives impurity scattering equivalent to 40% T_c suppression.

Transition into superconducting state is second order for weak scattering.

Strong scattering can induce first-order transitions into superconducting states.

Abstract

We calculate the Pauli-limited upper critical field and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) instability for {\it dirty} d-wave superconductors within the quasiclassical theory using the self-consistent $\hat{t}$-matrix approximation for impurities. We find that the phase diagram depends sensitively on the scattering rate and phase shift of nonmagnetic impurities. The transition into the superconducting state is always second order for weak (Born) scattering, while in the unitarity (strong) scattering limit a first-order transition into both uniform and spatially modulated superconducting states is stabilized. Contrary to general belief, we find that the FFLO phase is robust against disorder and survives impurity scattering equivalent to a $T_c$ suppression of roughly 40%. Our results bear on the search of FFLO states in heavy-fermion and layered organic superconductors.