Keldysh action for disordered superconductors
Abstract
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 8×8 matrix Q(t,t') 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 wellknown result for the Coulombinduced renormalization of the electronelectron 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 twodimensional 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 zerobias anomaly in the density of states and disorderenhanced repulsion in the Cooper channel.
 Publication:

Physical Review B
 Pub Date:
 May 2000
 DOI:
 10.1103/PhysRevB.61.12361
 arXiv:
 arXiv:condmat/9907358
 Bibcode:
 2000PhRvB..6112361F
 Keywords:

 74.40.+k;
 74.50.+r;
 72.10.Bg;
 Fluctuations;
 Tunneling phenomena;
 point contacts weak links Josephson effects;
 General formulation of transport theory;
 Condensed Matter  Superconductivity;
 Condensed Matter  Mesoscale and Nanoscale Physics
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