Impurities and Quasi-One-Dimensional Transport in ad-Wave Superconductor

Abstract

Impurity scattering in the unitary limit produces low-energy quasiparticles with an anisotropic spectrum in a two-dimensional $d$-wave superconductor. We describe a new quasi-one-dimensional limit of the quasiparticle scattering, which might occur in a superconductor with short coherence length and with finite impurity potential range. The dc conductivity in a $d$-wave superconductor is predicted to be proportional to the normal state scattering time and is impurity dependent. The quasi-one-dimensional regime will occur in high-$T_c$ superconductors above critical impurity concentration. We argue that the impurities produce weak orthogonal localization of the quasiparticles.