# Effective lattice model for collective modes in a Fermi liquid with spin-orbit coupling

## TL;DR

This paper models chiral spin waves in a two-dimensional Fermi liquid with spin-orbit coupling using an effective tight-binding lattice model, revealing how collective modes emerge from defect interactions.

## Contribution

It introduces a novel mapping of kinetic equations to a tight-binding lattice model to analyze collective spin modes with spin-orbit coupling.

## Key findings

- Effective tight-binding model captures collective mode spectrum.
- Spin-flip excitations form a conduction band in the lattice analogy.
- Interactions are represented as lattice defects affecting collective modes.

## Abstract

A Fermi-liquid (FL) with spin-orbit coupling (SOC) supports a special type of collective modes--chiral spin waves--which are oscillations of magnetization even in the absence of the external magnetic field. We study the chiral spin waves of a two-dimensional FL in the presence of both the Rashba and Dresselhaus types of SOC and also subject to the in-plane magnetic field. We map the system of coupled kinetic equations for the angular harmonics of the occupation number onto an effective one-dimensional tight-binding model, in which the lattice sites correspond to angular-momentum channels. Linear-in-momentum SOC ensures that the effective tight-binding model has only nearest-neighbor hopping on a bipartite lattice. In this language, the continuum of spin-flip particle-hole excitations becomes a conduction band of the lattice model, whereas electron-electron interaction, parameterized by the harmonics of the Landau function, is mapped onto lattice defects of both on-site and bond type. Collective modes correspond to bound states formed by such defects. All the features of the collective-mode spectrum receive natural explanation in the lattice picture as resulting from the competition between on-site and bond defects.