Exact summation of vertex corrections to the penetration depth in d-wave superconductors

TL;DR

This paper derives an exact, simplified relationship between the penetration depth and quasiparticle density of states in d-wave superconductors with forward impurity scattering, relevant for high-purity cuprate crystals.

Contribution

It introduces a zero-angle scattering approximation to sum vertex corrections exactly in the calculation of the penetration depth in disordered d-wave superconductors.

Findings

Exact relationship between normal fluid density and density of states

Applicable to high-purity underdoped YBCO crystals

Simplifies understanding of impurity effects on penetration depth

Abstract

A variety of experiments suggest that in the cuprates, the low-energy superconducting quasiparticles undergo forward scattering from extended impurity potentials. We argue that when such potentials dominate the scattering, the penetration depth may be computed in a simple zero-angle scattering approximation (ZSA), in which the vertex corrections to the Meissner effect may be summed exactly. We find a remarkably simple relationship between the normal fluid density and the quasiparticle density of states of the disordered system which holds for every realization of the disorder. We expect this result to be relevant to the $ab$-plane penetration depth in high-purity single crystals of underdoped YBCO.