Theory of a chiral Fermi liquid: general formalism

TL;DR

This paper extends Fermi-liquid theory to systems with spin-orbit coupling, deriving a formalism that accounts for spin-split bands and analyzing how spin and charge properties are affected, especially under Rashba coupling.

Contribution

It develops a general formalism for chiral Fermi liquids with spin-orbit coupling, including a phenomenological Landau function and analysis of quasiparticle properties.

Findings

Charge-sector properties are determined by well-defined quasiparticles.

Spin-sector properties involve contributions from damped states, especially with stronger SO coupling.

Spin-splitting of Fermi velocities arises due to the Kohn anomaly affected by SO coupling.

Abstract

We extend the Fermi-liquid (FL) theory to include spin-orbit (SO) splitting of the energy bands, focusing on the Rashba SO coupling as an example. We construct the phenomenological Landau interaction function for such a system using the symmetry arguments and verify this construction by an explicit perturbative calculation. The Landau function is used to obtain the effective mass, compressibility, and stability conditions of the FL. It is shown that although the charge-sector properties, such as the effective mass and compressibility, are determined solely by well-defined quasiparticles, the spin-sector properties, such as the spin susceptibility, contain a contribution from damped states in between the spin-split Fermi surfaces, and thus cannot be fully described by the FL theory, except for the case of weak SO coupling. We derive some specific properties of a chiral FL and show, in particular, that for contact interaction spin-splitting of the Fermi velocities of Rashba subbands occurs because of the Kohn anomaly, also modified by SO coupling.