Eur. Phys. J. B 10, 247-255 (1999)
https://doi.org/10.1007/s100510050852

The physical origin of the electron-phonon vertex correction

¹ Dipartimento di Fisica, Università di Roma I "La Sapienza", Piazzale A. Moro 2, 00185 Roma, Italy
² Istituto Nazionale Fisica della Materia, Unità di Roma 1, Piazzale A. Moro 2, 00185 Roma, Italy

Corresponding author: ^a claudio.grimaldi@epfl.ch

Received: 23 November 1998
Revised: 22 January 1999
Published online: 15 July 1999

Abstract

In the theory of nonadiabatic superconductivity several features are governed by the electron-phonon vertex correction which has a complex structure both in momentum and frequency. We derive a physical interpretation of such nonadiabatic effects that permits to link them to specific material properties. We show how the nonadiabatic vertex correction can be decomposed into two terms with different physical origins. In particular, the first term describes the lattice polarization induced by the electrons and it is essentially a single-electron process whereas the second term is governed by the particle-hole excitations due to the exchange part of the phonon-mediated electron-electron interaction. We show that by weakening the influence of the exchange interaction the vertex takes mostly positive values giving rise to an enhanced effective coupling in the scattering with phonons. This weakening of the exchange interaction can be obtained by lowering the density of the electrons, or by considering only long-ranged (small q) electron-phonon couplings.