Renormalization group and the superconducting susceptibility of a Fermi liquid

S. A. Parameswaran, R. Shankar, Shivaji Lal Sondhi

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

A free Fermi gas has, famously, a superconducting susceptibility that diverges logarithmically at zero temperature. In this paper we ask whether this is still true for a Fermi liquid and find that the answer is that it does not. From the perspective of the renormalization group for interacting fermions, the question arises because a repulsive interaction in the Cooper channel is a marginally irrelevant operator at the Fermi liquid fixed point and thus is also expected to infect various physical quantities with logarithms. Somewhat surprisingly, at least from the renormalization group viewpoint, the result for the superconducting susceptibility is that two logarithms are not better than one. In the course of this investigation we derive a Callan-Symanzik equation for the repulsive Fermi liquid using the momentum-shell renormalization group, and use it to compute the long-wavelength behavior of the superconducting correlation function in the emergent low-energy theory. We expect this technique to be of broader interest.

Original languageEnglish (US)
Article number195104
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume82
Issue number19
DOIs
StatePublished - Nov 4 2010

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Fingerprint Dive into the research topics of 'Renormalization group and the superconducting susceptibility of a Fermi liquid'. Together they form a unique fingerprint.

Cite this