Field theoretic formulation and soft modes of dirty superconductors

Abstract

Basic physical properties of the ordered phase of dirty superconductors are analyzed by means of field theoretic and complementing diagrammatic methods. Disorder-generated diffusive singularities are shown to be preserved in several two-particle correlations for all temperatures in the superconducting phase and within the band of one-electron states. The smooth crossover of the diffusion constant through the transition is given. The presence of the diffusive singularities is related toi) a restricted rotational invariance of a BCS-decoupled effective Lagrangian for the gap phase andii) generally to Nambu's generalized Ward identity (GWI). By explicit calculation under control of the GWI the coexistence of the diffusive mode with a propagating mode of Bogoliubov-Anderson type is found. The dispersion relation Ω(q)=γq for the collective oscillation of the superfluid Cooper pairs is calculated in the largen limit of then orbital model. The crossover to a soft plasmon-like mode in less than three dimensions and due to the long-range Coulomb repulsion is briefly discussed.

The Lagrangian field theory, based on work by Schäfer, Wegner, Efetov, and Finkelstein, is devised for a description of disorder effects in superconducting and/or ferromagnetic phases. At the level of decoupled interaction a superconductor-insulator transition due to localization of Cooper pairs at zero temperature is suggested. Charge conservation is guaranteed by the GWI superimposed as a dynamic self-consistency condition. In the largen limit the coexistence phase of a dirty itinerant ferromagnetic superconductor is found to be unstable as in the BCS-Stoner theory of Lei, Ting, and Birman for clean systems.