The Ward identity and nonadiabatic corrections to the quasiparticle self-energy

TL;DR

This paper explores the applicability of a gauge-invariant self-consistent method for calculating quasiparticle self-energy in materials where phonon and electron energies are comparable, addressing nonadiabatic effects.

Contribution

It analyzes the conditions under which the gauge-invariant self-consistent approach is valid for nonadiabatic corrections in complex materials.

Findings

Identifies key conditions for the method's applicability.

Highlights importance of nonadiabatic effects in certain materials.

Provides theoretical insights into quasiparticle self-energy calculations.

Abstract

In some newly discovered materials the ratio of phonon to electron energies is no longer small. We have investigated the basement of the recently proposed gauge-invariant self-consistent method and found conditions of its applicability.