Kinetic processes in Fermi-Luttinger liquids

Abstract

In this work we discuss extensions of the pioneering analysis by Dzyaloshinski ǐ and Larkin [Sov. Phys. JETP 38, 202 (1974)] 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.For the special issue of JETP devoted to the 90th birthday jubilee of Igor E. Dzyaloshinski ǐ.1) Throughout the paper we use units with Planck and Boltzmann constants set to unity = k B = 1.

Quasiparticle energy relaxation in a gas of one-dimensional fermions with Coulomb interaction

“…Recent theoretical progress has shown the importance of the nonlinear corrections to the spectrum, as they affect response functions and enable quasiparticle relaxation [3,4]. Experiments with one-dimensional conductors support these findings.…”