Coupled spin-charge dynamics in helical Fermi liquids beyond the random phase approximation

TL;DR

This paper develops a theoretical framework to analyze coupled spin-charge dynamics in helical Fermi liquids, extending beyond the random phase approximation to accurately describe collective modes and response functions.

Contribution

It introduces a coupled spin-charge response matrix approach that incorporates local-field corrections, providing a more precise description of collective excitations in helical systems.

Findings

Accurately predicts collective spin-charge modes in Rashba systems.

Shows good agreement with existing methods for Drude weight and spin-Hall conductivity.

Extends RPA to include local-field effects for better modeling of spin-charge interactions.

Abstract

We consider a helical system of fermions with a generic spin (or pseudospin) orbit coupling. Using the equation of motion approach for the single-particle distribution functions, and a mean-field decoupling of the higher order distribution functions, we find a closed form for the charge and spin density fluctuations in terms of the charge and spin density linear response functions. Approximating the nonlocal exchange term with a Hubbard-like local-field factor, we obtain coupled spin and charge density response matrix beyond the random phase approximation, whose poles give the dispersion of four collective spin-charge modes. We apply our generic technique to the well-explored two-dimensional system with Rashba spin-orbit coupling and illustrate how it gives results for the collective modes, Drude weight, and spin-Hall conductivity which are in very good agreement with the results obtained from other more sophisticated approaches.