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Anderson localization problems in gapless superconducting phases

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  • Oppenmann, R.

Abstract

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.

Suggested Citation

  • Oppenmann, R., 1990. "Anderson localization problems in gapless superconducting phases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 167(1), pages 301-312.
    • Handle: RePEc:eee:phsmap:v:167:y:1990:i:1:p:301-312
    DOI: 10.1016/0378-4371(90)90061-V
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