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Zero sound origin of acoustic plasmons in two-component Fermi gases

A. N. Afanasiev

Published May 12, 2021• 0 citations
OpenAlex

Abstract

Collective density excitation spectrum in two-component Fermi gases is dominated by conventional optical plasmon at high frequencies and charge neutral gapless acoustic mode in the quasi-classical domain. In this work we reveal the identity between the latter acoustic plasmon and zero sound propagating in the slow component. Within the framework of two coupled collisionless kinetic equations with self-consistent electrostatic potential, we show that the mode stability to the long-range intracomponent Coulomb interaction is determined by the static screening by the fast quasiparticles. Depending on the magnitude of the effective Landau interaction parameter given by the ratio of Thomas-Fermi wavevectors in components, acoustic plasmon undergoes transformation from zero sound in almost ideal Fermi gas to ion-acoustic wave in both two and three dimensions. As it was recently shown for the particular case of type-I Weyl semimetals [Afanasiev, Greshnov and Svintsov, Phys. Rev. B 103, 205201 (2021)], strongly anisotropic two-component solid state plasma is a natural platform hosting this acoustic plasmon-zero sound mode which is experimentally accessible via standard energy-loss and time-domain techniques.

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Atypical behavior of collective modes in two-dimensional Fermi liquids

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Collective Modes in Bose-Fermi Mixture Gases

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This thesis theoretically deals with collective modes in the normal phase of a Bose-Fermi mixture composed of single-species bosons and single-species fermions.The mixture is experimentally established as an ultracold atomic gas.While the community studies the mixture including a superfluid phase, relevant to Bose-Einstein condensation of bosons and Cooper paring of fermions, dynamical behaviors in the normal phase have been not fully understood so that we are interested in.We consider the mixture in both spatially uniform and harmonically trapped systems with the Boltzmann equation at finite temperatures.We perform the analysis under the assumption that the physical quantities are near to equilibrium.After the linerization, we apply the moment method to the equation, obtaining a closed set of coupled equations to describe sound or oscillation.The collisional property of the system characterizes the collective modes in the sense of the hydrodynamic regime, collisionless regime, and transition between these regimes.In the uniform system, we investigate sound mode and the dynamic density structure factor.With decreasing temperature, we find that the sound velocity deviates from that of the hydrodynamic mode.Even at a temperature much lower than the Fermi temperature, the sound velocity does not reach the collisionless limit analogous to the zero sound in a Fermi system.However, we show the existence of a long-lived sound at a low temperature as distinct from the first and zero sounds.Nature of the long-lived sound seems to be originated by Pauli blocking of fermions; this statistical effect makes the interspecies collision suppress in the Bose-Fermi mixture.In the trapped system, we mainly study dipole oscillation.We consistently define the relaxation time originated by the interspecies scattering.We find that two oscillating modes in the collisionless regime have distinct fates in the hydrodynamic regime; one collisionless mode shows a crossover to a hydrodynamic in-phase mode, and the other collisionless mode shows a transition to two purely-damped modes.We show the time evolution of the three types of hydrodynamic modes with suitable initial conditions.We discuss temperature dependence of the dipole modes.We observe that the relaxation time dominates the dependence compared to the mean-field contribution.We also observe the nonmonotonic behavior of the relaxation time when Pauli blocking of fermions is not negligible.i List of Figures 1.1 Two schematic images of collisions with a period of oscillation . . . . . . . . . . . . . . . . 1 1.2 Measurement of the zero sound in pure liquid 3 He . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Transition between the first sound and the zero sound in a two-component Fermi gas . . . 3 1.4 Dipole oscillations of the two-component gas of 40 K . . . . . . . . . . . . . . . . . . . . . . 4 1.5 Frequencies of dipole mode in the two-component gas of 40 K . . . . . . . . . . . . . . . . . 4 1.6 Damping times of dipole mode in the two-component gas of 40 K . . . . . . . . . . . . . . . 5 1.7 Dipole oscillations of the mixture of 87 Rb and 40 K in the hydrodynamic regime . . . . . . .6 1.8 Dipole oscillations of the mixture of 87 Rb and 40 K in the deeper hydrodynamic regime . . .6 1.9 Dipole oscillations of the mixture of 87 Rb and 40 K in the collisionless regime . . . . . . . .7 2.1 Results obtained by solving the coupled moment equations for sound mode . . . . . . . . .26 3.1 Time evolution of the center-of-mass positions and velocity fields . . . . . . . . . . . . . .39 3.2 Dipole modes as a function of the relaxation time with N B = N F . . . . . . . . . . . . . . .40 3.3 Dipole modes as a function of the relaxation time with N B /N F = 0.2 . . . . . . . . . . . . .41 3.4 Ratio of the displacement of the center of mass to the velocity field as a function of the relaxation time . . . . . . . . . . . . . . . . . . .

•Mar 17, 2020•0 citations

SOUND PROPAGATION IN A DILUTE FERMI GAS AT ZERO TEMPERATURE

Kurt Gottfried, L. Pičman

Landau showed that a nonideal Fermi gas at zero temperature can sustain collective oscillations of the acoustical type (zeroth sound). The altenuation of zeroth sound in a dilute Fermi gas with repulive intereacitions was considered. The problem was formulted interms of the Green function G which describes the paropation of density fluctuations through the system. The simplest approximation of G led to Landau's dispersion law which wae analyzed in some detail. The contribution of the phonons' zero point oscillations to the ground- state energy was estimated and found to lead to a term which has an essential singuarty at the origin of the coupling constant plane. The energy and width of the phonon are given by the poles in the spectral representation of G, and the location of these poles was determined from the Fredholm solution of an apparoximate integral equation satisfied by G. In this way it is showa that ths width, divided by the displacement of the collective state above the single- particle continunna of the free gas, vanishes linearly in the long wavelength limit. It is also shows that in the limit of extreme dilution the correct damping; can be obtained by merely taking the finite lifetimemore » of single-particles excitations into account and ignoring the dissipative effects of the noninstantaneous interactions betweein the particles in the medium. Finally, it is alao argued that the Fredholm method is the natural tool for discussing many problems in the theory of collective motion. (auth)« less

•Jan 1, 1960•2 citations
Collective density excitation spectrum in two-component Fermi gases is dominated by conventional optical plasmon at high frequencies and charge neutral gapless acoustic mode in the quasi-classical domain. In this work we reveal the identity between the latter acoustic plasmon and zero sound propagating in the slow component. Within the framework of two coupled collisionless kinetic equations with self-consistent electrostatic potential, we show that the mode stability to the long-range intracomponent Coulomb interaction is determined by the static screening by the fast quasiparticles. Depending on the magnitude of the effective Landau interaction parameter given by the ratio of Thomas-Fermi wavevectors in components, acoustic plasmon undergoes transformation from zero sound in almost ideal Fermi gas to ion-acoustic wave in both two and three dimensions. As it was recently shown for the particular case of type-I Weyl semimetals [Afanasiev, Greshnov and Svintsov, Phys. Rev. B 103, 205201 (2021)], strongly anisotropic two-component solid state plasma is a natural platform hosting this acoustic plasmon-zero sound mode which is experimentally accessible via standard energy-loss and time-domain techniques.
The dispersion equation for acoustic plasmons in a high-density degenerate two-component Fermi gas is given and analysed. The random phase approximation (RPA) dielectric function is used, with exact analytic continuation from the upper to the lower half of the complex frequency plane. For small wavevector the acoustic plasmon frequency and damping depend on only two parameters, the ratio of Fermi velocities and the ratio of Thomas-Fermi wavevectors. A large mass ratio is not necessary for weak damping.
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.
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.
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.
This thesis theoretically deals with collective modes in the normal phase of a Bose-Fermi mixture composed of single-species bosons and single-species fermions.The mixture is experimentally established as an ultracold atomic gas.While the community studies the mixture including a superfluid phase, relevant to Bose-Einstein condensation of bosons and Cooper paring of fermions, dynamical behaviors in the normal phase have been not fully understood so that we are interested in.We consider the mixture in both spatially uniform and harmonically trapped systems with the Boltzmann equation at finite temperatures.We perform the analysis under the assumption that the physical quantities are near to equilibrium.After the linerization, we apply the moment method to the equation, obtaining a closed set of coupled equations to describe sound or oscillation.The collisional property of the system characterizes the collective modes in the sense of the hydrodynamic regime, collisionless regime, and transition between these regimes.In the uniform system, we investigate sound mode and the dynamic density structure factor.With decreasing temperature, we find that the sound velocity deviates from that of the hydrodynamic mode.Even at a temperature much lower than the Fermi temperature, the sound velocity does not reach the collisionless limit analogous to the zero sound in a Fermi system.However, we show the existence of a long-lived sound at a low temperature as distinct from the first and zero sounds.Nature of the long-lived sound seems to be originated by Pauli blocking of fermions; this statistical effect makes the interspecies collision suppress in the Bose-Fermi mixture.In the trapped system, we mainly study dipole oscillation.We consistently define the relaxation time originated by the interspecies scattering.We find that two oscillating modes in the collisionless regime have distinct fates in the hydrodynamic regime; one collisionless mode shows a crossover to a hydrodynamic in-phase mode, and the other collisionless mode shows a transition to two purely-damped modes.We show the time evolution of the three types of hydrodynamic modes with suitable initial conditions.We discuss temperature dependence of the dipole modes.We observe that the relaxation time dominates the dependence compared to the mean-field contribution.We also observe the nonmonotonic behavior of the relaxation time when Pauli blocking of fermions is not negligible.i List of Figures 1.1 Two schematic images of collisions with a period of oscillation . . . . . . . . . . . . . . . . 1 1.2 Measurement of the zero sound in pure liquid 3 He . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Transition between the first sound and the zero sound in a two-component Fermi gas . . . 3 1.4 Dipole oscillations of the two-component gas of 40 K . . . . . . . . . . . . . . . . . . . . . . 4 1.5 Frequencies of dipole mode in the two-component gas of 40 K . . . . . . . . . . . . . . . . . 4 1.6 Damping times of dipole mode in the two-component gas of 40 K . . . . . . . . . . . . . . . 5 1.7 Dipole oscillations of the mixture of 87 Rb and 40 K in the hydrodynamic regime . . . . . . .6 1.8 Dipole oscillations of the mixture of 87 Rb and 40 K in the deeper hydrodynamic regime . . .6 1.9 Dipole oscillations of the mixture of 87 Rb and 40 K in the collisionless regime . . . . . . . .7 2.1 Results obtained by solving the coupled moment equations for sound mode . . . . . . . . .26 3.1 Time evolution of the center-of-mass positions and velocity fields . . . . . . . . . . . . . .39 3.2 Dipole modes as a function of the relaxation time with N B = N F . . . . . . . . . . . . . . .40 3.3 Dipole modes as a function of the relaxation time with N B /N F = 0.2 . . . . . . . . . . . . .41 3.4 Ratio of the displacement of the center of mass to the velocity field as a function of the relaxation time . . . . . . . . . . . . . . . . . . .
Landau showed that a nonideal Fermi gas at zero temperature can sustain collective oscillations of the acoustical type (zeroth sound). The altenuation of zeroth sound in a dilute Fermi gas with repulive intereacitions was considered. The problem was formulted interms of the Green function G which describes the paropation of density fluctuations through the system. The simplest approximation of G led to Landau's dispersion law which wae analyzed in some detail. The contribution of the phonons' zero point oscillations to the ground- state energy was estimated and found to lead to a term which has an essential singuarty at the origin of the coupling constant plane. The energy and width of the phonon are given by the poles in the spectral representation of G, and the location of these poles was determined from the Fredholm solution of an apparoximate integral equation satisfied by G. In this way it is showa that ths width, divided by the displacement of the collective state above the single- particle continunna of the free gas, vanishes linearly in the long wavelength limit. It is also shows that in the limit of extreme dilution the correct damping; can be obtained by merely taking the finite lifetimemore » of single-particles excitations into account and ignoring the dissipative effects of the noninstantaneous interactions betweein the particles in the medium. Finally, it is alao argued that the Fredholm method is the natural tool for discussing many problems in the theory of collective motion. (auth)« less