Residual absorption at zero temperature in d-wave superconductors

TL;DR

This paper explains residual optical absorption at zero temperature in d-wave superconductors due to impurity scattering, revealing characteristic features in conductivity and superfluid density that match recent experimental data.

Contribution

It provides a theoretical analysis of residual absorption in d-wave superconductors with impurities, bridging the gap between weak and strong scattering regimes.

Findings

Significant residual oscillator strength remains at zero temperature.

Optical conductivity exhibits a cusp-like behavior with upward curvature.

Superfluid density shows a quasilinear temperature dependence.

Abstract

In a d-wave superconductor with elastic impurity scattering, not all the available optical spectral weight goes into the condensate at zero temperature, and this leads to residual absorption. We find that for a range of impurity parameters in the intermediate coupling regime between Born (weak) and unitary (strong) limit, significant oscillator strength remains which exhibits a cusp like behavior of the real part of the optical conductivity with upward curvature as a function of frequency, as well as a quasilinear temperature dependence of the superfluid density. The calculations offer an explanation of recent data on ortho-II YBa$_2$Cu$_3$O$_{6.5}$ which has been considered anomalous.