ANDERSON LOCALIZATION PROBLEMS IN GAPLESS SUPERCONDUCTING PHASES

The interplay of Anderson localization and different kinds of superconducting order is most interesting in "gapless" cases, i.e. for nonvanishing electron density of states at EF. I present a new renormalization group result for Anderson localization in the gapless type II limit of an Ising superconducting (SC) glass. From this calculation a guess is also made for the XY superconducting glass. In both cases, and in contrast to localization in normal systems, two renormalization constants (one for field- and one for coupling constant renormalization) are necessary (and sufficient). The density of states at EF is singular with exponent β. For the Ising SC-glass I obtain vI = 1/(d - 2), βI = 1/2, and ηI = 0, while the XY SC-glass has vXY = 1/(d - 2), βXY = 1, and ηXY = d - 2, all in leading order of the d - 2 expansion and for E = EF. For E≠EF a symmetry argument, and also the calculation given here, predict usual localization behaviour with v = 1/(d - 2), β = 0, and η = 2 - d in both cases. The effects of Cooper pairs on localization in the pure superconducting glasses is compared with earlier results showing perfect coexistence of Anderson localization with dirty superconductivity approximately described by a nonrandom order parameter. These limiting cases are embedded in a more general field theory given here, which contains three superconducting order parameters and a conventional pair-breaking mechanism. © 1990.