Penetration-depth anisotropy in unconventional superconductors.

Abstract

We consider the superfluid density tensor in a three-dimensional superconductor, as a function of temperature and impurity concentration. We compare the results for two different order parameters: an anisotropic {ital s}-wave gap {Delta}{sub {ital s}}(@k{cflx R}), and a {ital d}-wave gap {Delta}{sub {ital d}}(@k{cflx R}) with {Delta}{sub {ital s}}(@k{cflx R})={vert_bar}{Delta}{sub {ital d}}(@k{cflx R}){vert_bar}. While the two order parameters yield identical {rho}(spec. char. missing) tensors in the pure limit, we find that the addition of impurities affects the two cases very differently. In particular, the behavior of the anisotropy distinguishes the two order parameters. Thus measurements of the anisotropy as a function of impurity concentration can be a key to identifying the order-parameter symmetry. We also discover a surprising result: the addition of impurities can increase one of the principal values of {rho}(spec. char. missing){sub {ital s}}, in the {ital s}-wave case.