Eliashberg Theory: a short review

TL;DR

Eliashberg theory extends BCS superconductivity by incorporating phonon dynamics and retardation effects, resulting in a frequency-dependent order parameter and providing a more detailed understanding of electron-phonon interactions in superconductors.

Contribution

This review summarizes the finite temperature formulation of Eliashberg theory on both imaginary and real frequency axes, highlighting its implications and areas needing further research.

Findings

Demonstrates the impact of phonon dynamics on superconducting properties

Shows the frequency dependence of the order parameter in Eliashberg theory

Identifies assumptions in the theory that require further validation

Abstract

Eliashberg theory is a theory of superconductivity that describes the role of phonons in providing the attractive interaction between two electrons. Phonon dynamics are taken into account, thus giving rise to retardation effects that impact the electrons, in the form of a frequency-dependent electron self-energy. In the superconducting state, this means that the order parameter, generally considered to be a static quantity in the Bardeen-Cooper-Schrieffer (BCS) theory, also becomes frequency-dependent. Here we review the finite temperature formulation of Eliashberg theory, both on the imaginary and real frequency axis, and briefly display some examples of the consequences of a dynamical, as opposed to static, interaction. Along the way we point out where further work is required, concerning the validity of some of the assumptions used.