Keldysh action for disordered superconductors

M. Feigel’man, A. Larkin

Research output: Contribution to journalArticlepeer-review

70 Citations (Scopus)


The Keldysh representation of the functional integral for the interacting electron system with disorder is used to derive microscopically an effective action for dirty superconductors. In the most general case this action is a functional of the (Formula presented) matrix (Formula presented) which depends on two time variables, and on the fluctuating order parameter field and electric potential. We show that this approach reproduces, without the use of the replica trick, the well-known result for the Coulomb-induced renormalization of the electron-electron coupling constant in the Cooper channel. Turning to the results, we calculate the effects of the Coulomb interaction upon (i) the subgap Andreev conductance between the superconductor and the two-dimensional dirty normal metal, and (ii) the Josephson proximity coupling between superconductive islands via such a metal. These quantities are shown to be strongly suppressed by the Coulomb interaction at sufficiently low temperatures due to both zero-bias anomaly in the density of states and disorder-enhanced repulsion in the Cooper channel.

Original languageEnglish
Pages (from-to)12361-12388
Number of pages28
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number18
Publication statusPublished - 2000
Externally publishedYes


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