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Low Temperature Physics

Long-wave fluctuation kinetics and quasi-linear relaxation for zero-point sound in a normal Fermi liquid

Yu. V. Slyusarenko

Published Jun 1, 1998• 3 citations
Publisher

Abstract

A universal phenomenological approach to studying macroscopic fluctuations is proposed and general kinetic equations for long-wave fluctuations in a normal Fermi liquid are derived. These kinetic equations form the basis of the theory of quasi-linear relaxation for zero-point sound in a normal Fermi liquid in the paired fluctuation approximation. The conditions for the existence of the quasi-linear approximation are considered.

DOI
10.1063/1.593607

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A universal phenomenological approach to studying macroscopic fluctuations is proposed and general kinetic equations for long-wave fluctuations in a normal Fermi liquid are derived. These kinetic equations form the basis of the theory of quasi-linear relaxation for zero-point sound in a normal Fermi liquid in the paired fluctuation approximation. The conditions for the existence of the quasi-linear approximation are considered.
Marginal Fermi liquid was originally introduced as a phenomenological description of the cuprates in a part of the metallic doping range which appears to be governed by fluctuations due to a quantum-critical point. An essential result due to the form of the assumed fluctuation spectra is that the large inelastic quasiparticle relaxation rate near the Fermi surface is proportional to the energy measured from the chemical potential, ${\ensuremath{\tau}}_{i}^{\ensuremath{-}1}\ensuremath{\propto}\ensuremath{\epsilon}$. We present a microscopic long-wavelength derivation of the hydrodynamic properties in such a situation by an extension of the procedure that Eliashberg used for the derivation of the hydrodynamic properties of a Landau-Fermi liquid. In particular, the density-density and the current-current correlations and the relation between the two are derived, and the connection to microscopic calculations of the frequency dependence of the optical conductivity with an additional Fermi-liquid correction factor shown to follow. The method used here may be necessary, quite generally, for the correct hydrodynamic theory for any problem of quantum-critical fluctuations in fermions.
We study the appearance of a sharp collective mode which features transverse current fluctuations within the bosonization approach to interacting two-dimensional Fermi liquids. This mode is analogous to the shear sound modes in elastic media, and, unlike the conventional zero sound mode, it is damped in weakly interacting Fermi liquids and only separates away from the particle-hole continuum when the quasiparticle mass becomes twice the transport mass ${m}^{*}\ensuremath{\gtrsim}2m$. The shear sound should be present in a large class of interacting charged and neutral Fermi liquids especially those proximate to critical points where the quasiparticle mass diverges. In metals this mode remains linearly dispersing in the presence of the long-ranged Coulomb force, unlike the conventional zero sound mode which becomes the plasma mode. We also detail a quick path between bosonization and classical Landau's Fermi liquid theory by constructing a mapping between the solutions of the classical kinetic equation and the quantized bosonic eigenmodes. By further mapping the kinetic equation into a one-dimensional tight-binding model we solve for the entire spectrum of collective and incoherent particle-hole excitations of Fermi liquids with nonzero F0{F}_{0}F0​ and F1{F}_{1}F1​ Landau parameters.
The phenomenological theory of a Fermi liquid is generalized to nonequilibrium conditions. Landau's theory is reformulated to include fluctuations of the distribution function and quasiparticle energy. The method of fluctuation in kinetic equations is used to establish the collision integral of the quasiparticle Boltzmann equation. This collision integral is expressed in terms of the parameters of Landau's theory, and includes dynamic screening effects. The results are compared with recent theories of transport in Fermi liquids.