Calculations for an inhomogeneous d-wave superconductor

We calculate the distributions P[Δ0(ri)] of local d-wave pairing amplitude Δ0(ri) at a position ri inside a disordered high-temperature superconductor (HTS) family. To reproduce the observed inhomogeneity a random potential Vimp, within a Bogoliubov-deGennes (BdG) formalism, is considered. We perform calculations with fixed values of the disorder strength Vimp obtaining the distribution of Δ0(ri), and local density of charge carriers ρ(ri), for different compounds of the LSCO family. The calculation of the relative root-mean-square deviation shows that the underdoped compounds are more inhomogeneous than the overdoped ones. Also, the spatial variation of Δ0(ri) decreases as the average density of charge carriers 〈ρ〉 increases, demonstrating that the compounds are more homogeneous for high values of 〈ρ〉. The results indicate that the d-wave superconducting gaps seem to be more sensitive to a change in the disorder in comparison with the s-wave superconducting gaps.