Renormalization Group Approach to Strong-Coupled Superconductors

Details Renormalization Group Approach to Strong-Coupled Superconductors Renormalization Group Approach to Strong-Coupled Superconductors

2004-06-07

arxiv.org/abs/cond-mat/0406174v2

Phys. Rev. B 72, 054531 (2005)

Physics

Condensed Matter

Superconductivity

6 pages, 3 figures, expanded presentation, final version

Scientific paper

10.1103/PhysRevB.72.054531

We develop an asymptotically exact renormalization group (RG) approach that treats electron-electron and electron-phonon interactions on equal footing. The approach allows an unbiased study of the instabilities of Fermi liquids without the assumption of a broken symmetry. We apply our method to the problem of strongly coupled superconductors and find the temperature T* below which the high-temperature Fermi liquid state becomes unstable towards Cooper pairing. We show that T* is the same as the critical temperature Tc obtained in Eliashberg's strong coupling theory starting from the low-temperature superconducting phase. We also show that Migdal's theorem is implicit in our approach. Finally, our results lead to a novel way to calculate numerically, from microscopic parameters, the transition temperature of superconductors.

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