Eur. Phys. J. B 33, 391-396 (2003)
https://doi.org/10.1140/epjb/e2003-00180-9

Renormalization of the electron-phonon interaction: a reformulation of the BCS-gap equation

Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany

Corresponding author: ^a huebsch@theory.phy.tu-dresden.de

Received: 11 September 2002
Revised: 13 December 2002
Published online: 3 July 2003

Abstract

A recently developed renormalization approach is used to study the electron-phonon coupling in many-electron systems. By starting from an Hamiltonian which includes a small gauge symmetry breaking field, we directly derive a BCS-like equation for the energy gap from the renormalization approach. The effective electron-electron interaction for Cooper pairs does not contain any singularities. Furthermore, it is found that phonon-induced particle-hole excitations only contribute to the attractive electron-electron interaction if their energy difference is smaller than the phonon energy.