Theoretical high-$T_c$ d-wave superconducting gap in an inhomogeneous medium

TL;DR

This paper presents a theoretical study of the distribution of local d-wave superconducting gaps in disordered high-$T_c$ superconductors, revealing inhomogeneity patterns consistent with experimental observations.

Contribution

It introduces a Bogoliubov-de Gennes formalism-based model to analyze inhomogeneity in high-$T_c$ superconductors considering disorder and doping levels.

Findings

Underdoped compounds are more inhomogeneous than overdoped ones.

Increasing average doping level leads to more homogeneous superconducting gaps.

The model reproduces experimental inhomogeneity patterns in HTSCs.

Abstract

We perform theoretical calculations to obtain a distribution of local d-wave superconducting gaps $\Delta_0({r})$ for a high temperature superconducting (HTSC) series in a disordered superconductor with an average doping level $<\rho>$. To reproduce the inhomogeneous medium a nonmagnetic random potential $V^{imp}$, within a Bogoliubov-de Gennes (BdG) formalism, is considered. First the phase diagram $\Delta_0 x <\rho>$ for the LSCO HTSC series, with V^{imp}=0, is obtained. Then, we perform calculations considering a fixed value of the disorder strength $V^{imp}$ and obtain a distribution of local superconducting gaps $\Delta_0({r})$, and local density of charge carriers $\rho({r})$. It is shown that the underdoped compounds are more inhomogeneous than the overdoped ones, which is in accordance with experimental findings. Also, the spatial variation of $\Delta_0({r})$ indicates that as <\rho> increases, the system becomes more homogeneous.