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Journal of Physics F Metal Physics

Acoustic plasmons in a two-component Fermi gas

Alan Cottey

Published Aug 1, 1985• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4608/15/8/001

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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.
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.
This paper is the first of two in which the coupled cluster method (CCM) or exp(S) formalism is applied to two-component Fermi systems, the aim being to describe real metals and superconductivity. In this paper the authors concentrate on exact results and restrict ourselves to a ring approximation, applicable essentially to a high-density regime. They show that in the ground-state formalism the random phase approximation (RPA) can be formulated as a system of coupled, bilinear integral equations satisfied by functions associated with the so-called four-point functions of the system which provide a measure of the two-particle two-hole components in the true ground-state wavefunction. These equations are analysed in the dimensionless parameter formed by the ratio of the species masses and exact analytic solutions obtained. For Coulombic potentials (V 11 V 22 =V 2 12 ) they show that the exact analytic solution is unique and obtain an expression for the correlation energy. For non-Coulombic potentials (V 11 V 22 not=V 2 12 ) they indicate how to obtain a possible analytic solution. An RPA-like treatment of the one- and two-body equations in the excited-state formalism is provided for completeness.
A multi-component, many-particle system with Coulomb interaction is described in terms of a generalized dielectric constant ε(q, ω). The ε(q, ω) is calculated by the use of the equation-of-motion of a correlation function obtained within the random phase approximation (R.P.A.). For the Fermi, Bose, Bose and Bose, and Bose and Fermi systems, the ε(q, ω) obatined above leads directly to the result of Gell-Mann and Brueckner, Foldy, Bassichis, and Ginoza and Kanazawa, respectively. As for the Fermi and Fermi system, it has two collective excitations: plasma wave and acoustic phonon wave. The latter is well-defined only for such a special choice of parameters specifying the system as vF1 ≫s > vF2 and further, for the choice of parameters as vF1 ≫s≫vF2, agrees with the acoustic phonon wave of an electronion system treated by the Thomas-Fermi approximation. For the parameters chosen otherwise, such a wave is unstable or does not exist. In the expressions of the conditions above, s is the velocity of acoustic phonon wave and vF1 and vF2 are Fremi velocities in one component and in the other, respectively. The above results show that in the weak coupling limit, the results obtained by treating Bose components consistently by the Bogoliubov method are equivalent to those obtained with the R.P.A.
We perform RPA (Random Phase Approximation) study of collective excitations in the bose-fermi mixed degenerate gas of Alkali-metal atoms at T = 0. The calculation is done by diagonalization in a model space composed of particle-hole type excitations from the ground state, the latter being obtained from the coupled Gross-Pitaevskii and Thomas-Fermi equations. We investigate strength distributions for different combinations of bose and fermi multipole (L) operators with L = 0,1,2,3. Transition densities and dynamical structure factors are calculated for collective excitations. Comparison with the sum rule prediction for the collective frequency is given. Time dependent behavior of the system after an external impulse is studied. Typeset using REVTEX 1 I.
We consider the density response of a trapped two-component Fermi gas. Combining the Bogoliubov-deGennes method with the random phase approximation allows the study of both collective and single-particle excitations. Calculating the density response across a wide range of interactions, we observe a crossover from a weakly interacting pair vibration mode to a strongly interacting Goldstone mode. The crossover is associated with a depressed collective mode frequency and an increased damping rate, in agreement with density response experiments performed in strongly interacting atomic gases.