Simulating Superconducting Properties of Overdoped Cuprates: the Role of Inhomogeneity

TL;DR

This study models overdoped cuprates using disordered d-wave superconductors within the BdG framework and SCTMA, revealing insights into superfluid density behavior and the impact of inhomogeneity on superconducting properties.

Contribution

It provides a comparative analysis of BdG and SCTMA methods for weak scatterers in overdoped cuprates, highlighting the role of inhomogeneity and system size effects.

Findings

SCTMA performs well except in highly disordered regimes.

Superfluid density shows quadratic temperature dependence despite disordered states.

Discrepancies with previous results are due to system size limitations.

Abstract

Theoretical studies of disordered $d$-wave superconductors have focused, with a few exceptions, on optimally doped models with strong scatterers. Addressing recent controversies about the nature of the overdoped cuprates, however, requires studies of the weaker scattering associated with dopant atoms. Here we study simple models of such systems in the self-consistent Bogoliubov-de Gennes (BdG) framework, and compare to disorder-averaged results using the self-consistent-T-matrix-approximation (SCTMA). Despite surprisingly linear in energy behavior of the low-energy density of states even for quite disordered systems, the superfluid density in such cases retains a quadratic low-temperature variation of the penetration depth, unlike other BdG results reported recently. We trace the discrepancy to smaller effective system size employed in that work. Overall, the SCTMA performs remarkably well, with the exception of highly disordered systems with strongly suppressed superfluid density. We explore this interesting region where gap inhomogeneity dominates measured superconducting properties, and compare with overdoped cuprates.