Gradient expansion approach to multiple-band Fermi liquids

TL;DR

This paper develops a systematic gradient expansion method to derive a reduced Keldysh equation for low-energy quasi-particle dynamics in multi-band Fermi liquids, incorporating Berry phase effects and electron correlations.

Contribution

It introduces a perturbative projection technique within the gradient expansion to derive a reduced kinetic equation for doubly degenerate bands, including electron correlation effects under the adiabatic assumption.

Findings

Derived a systematic reduced Keldysh equation for multi-band Fermi liquids.

Incorporated Berry phase effects into the quasi-particle dynamics.

Accounted for electron-electron interactions via the adiabatic Fermi liquid assumption.

Abstract

Promoted by the recent progress of Berry phase physics in spin galvanomagnetic communities, we develop a systematic derivation of the reduced Keldysh equation (RKE) which captures the low-energy dynamics of quasi-particles constrained within doubly degenerate bands forming a single Fermi surface. Specifically, we project out the fully occupied/empty band degrees of freedom perturbatively in the gradient expansion, whose coupling constant measures how a system is disequilibrated. As for the electron-electron interactions, however, we only employ the so-called adiabatic assumption of the Fermi liquid theory, so that the effect of electron correlations onto the adiabatic transport of quasi-particles, i.e. the hermitian (real) part of the self-energy, is taken into account in an unbiased manner.