Kinetic processes in Fermi-Luttinger liquids

TL;DR

This paper extends the analysis of correlation functions in one-dimensional Fermi systems by exploring quasiparticle relaxation, spin-charge interactions, and transport phenomena using nonlinear Luttinger liquid theory and related models.

Contribution

It introduces a comprehensive analysis of quasiparticle relaxation, spin-exchange effects, and transport mechanisms in Fermi-Luttinger liquids with nonlinear dispersion.

Findings

Calculated thermalization rates for quasiparticles.

Determined momentum transfer rates for spin-exchange processes.

Analyzed effects of various scattering mechanisms on transport properties.

Abstract

In this work we discuss extensions of the pioneering analysis by Dzyaloshinskii and Larkin of correlation functions for one-dimensional Fermi systems, focusing on the effects of quasiparticle relaxation enabled by a nonlinear dispersion. Throughout the work we employ both, the weakly interacting Fermi gas picture and nonlinear Luttinger liquid theory to describe attenuation of excitations and explore the fermion-boson duality between both approaches. Special attention is devoted to the role of spin-exchange processes, effects of interaction screening, and integrability. Thermalization rates for electron- and hole-like quasiparticles, as well as the decay rate of collective plasmon excitations and the momentum space mobility of spin excitations are calculated for various temperature regimes. The phenomenon of spin-charge drag is considered and the corresponding momentum transfer rate is determined. We further discuss how momentum relaxation due to several competing mechanisms, viz. triple electron collisions, electron-phonon scattering, and long-range inhomogeneities affect transport properties, and highlight energy transfer facilitated by plasmons from the perspective of the inhomogeneous Luttinger liquid model. Finally, we derive the full matrix of thermoelectric coefficients at the quantum critical point of the first conductance plateau transition, and address magnetoconductance in ballistic semiconductor nanowires with strong Rashba spin-orbit coupling.