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Journal of the Physical Society of Japan

Dynamical Effects of the Landau ParameterF2in Normal Fermi Liquids

S. Tasaki, Fukuo Yoshida

Published May 15, 1989• 1 citation
Publisher

Abstract

Collective density excitations are studied in Ferrni liquids, with particular attention to the role of the Landau parameter of the second order F 2 . The density response function χ( k , z ) including F 2 is obtained by solving the Landau transport equation in the collisionless regime. From comparison of it with an formal expression in the small wavenumber limit, a relation is pointed out between F 2 and a pair correlation function. It is also found that there exists a critical value of F 2 above which χ( k , z ) exhibits two poles outside the continuum region. Zero-sound modes and their intensities, as well as the dynamical structure factor S ( k ,ω), are evaluated below and above the critical value. Discussion is also given on the F 2 -dependence of S ( k ,ω) at non-zero wavenumbers.

DOI
10.1143/jpsj.58.1667

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Collective density excitations are studied in Ferrni liquids, with particular attention to the role of the Landau parameter of the second order F 2 . The density response function χ( k , z ) including F 2 is obtained by solving the Landau transport equation in the collisionless regime. From comparison of it with an formal expression in the small wavenumber limit, a relation is pointed out between F 2 and a pair correlation function. It is also found that there exists a critical value of F 2 above which χ( k , z ) exhibits two poles outside the continuum region. Zero-sound modes and their intensities, as well as the dynamical structure factor S ( k ,ω), are evaluated below and above the critical value. Discussion is also given on the F 2 -dependence of S ( k ,ω) at non-zero wavenumbers.
Abstract Using the Landau kinetic equation to study the non-equilibrium behavior of interacting Fermi systems is one of the crowning achievements of Landau’s Fermi liquid theory. While thorough study of transport modes has been done for standard three-dimensional Fermi liquids, an equally in-depth analysis for two dimensional Fermi liquids is lacking. In applying the Landau kinetic equation (LKE) to a two-dimensional Fermi liquid, we obtain unconventional behavior of the zero sound mode c 0 . As a function of the usual dimensionless parameter s = ω / q v F , we find two peculiar results: first, for | s | > 1 we see the propagation of an undamped mode for weakly interacting systems. This differs from the three dimensional case where an undamped mode only propagates for repulsive interactions and the mode experiences Landau damping for any arbitrary attractive interaction. Second, we find that regardless of interaction strength, a propagating mode is forbidden for | s | < 1. This is profoundly different from the three-dimensional case where a mode can propagate, albeit damped. In addition, we present a revised Pomeranchuk instability condition for a two-dimensional Fermi liquid as well as equations of motion for the fluid that follow directly from the LKE. In two dimensions, we find a constant minimum for all Landau parameters for ℓ ⩾ 1 which differs from the three dimensional case. Finally we discuss the effect of a Coulomb interaction on the system resulting in the plasmon frequency ω p exhibiting a crossover to the zero sound mode.
Using the Landau theory of Fermi liquids, we calculate the dynamic response of both a polarized and an unpolarized normal Fermi gas at zero temperature in the strongly interacting regime of large scattering length. We show that at small excitation energies the in phase (density) response is enhanced with respect to the ideal gas prediction due to the increased compressibility. Vice versa, the out of phase (spin) response is quenched as a consequence of the tendency of the system to pair opposite spins. The long wavelength behavior of the static structure factor is explicitly calculated. The results are compared with the predictions in the collisional and superfluid regimes. The emergence of a spin zero sound solution in the unpolarized normal phase is explicitly discussed.
We derive the quantum Boltzmann equation (QBE) by using generalized Landau-interaction parameters, obtained through the nonequilibrium Green's function technique. This is a generalization of the usual QBE formalism to non-Fermi liquid (NFL) systems, which do not have well-defined quasiparticles. We apply this framework to a controlled low-energy effective field theory for the Ising-nematic quantum critical point, in order to find the collective excitations of the critical Fermi surface in the collisionless regime. We also compute the nature of the dispersion after the addition of weak Coulomb interactions. The zero angular momentum longitudinal vibrations of the Fermi surface show a linear-in-wavenumber dispersion, which corresponds to the zero sound of Landau's Fermi liquid theory. The Coulomb interaction modifies it to a plasmon mode in the long-wavelength limit, which disperses as the square-root of the wavenumber. Remarkably, our results show that the zero sound and plasmon modes exhibit the same behaviour as in a Fermi liquid, although an NFL is fundamentally different from the former.
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