Hydrodynamical properties of surface excitations in Fermi liquids with velocity-dependent interaction

Georg M. Bruun, Charles W. Clark

Lan Yin

In this paper, collective excitations in a homogeneous fermion-fermion mixture with different Fermi surfaces are studied. In the Fermi liquid phase, the zero-sound velocity is found to be larger than the largest Fermi velocity. With attractive interactions, the superfluid phase appears below a critical temperature, and the phase mode is the low-energy collective excitation. The velocity of the phase mode is significantly different from the zero-sound velocity. The difference between the two velocities may serve as a tool to detect the superfluid phase.

Henning Esbensen, G. F. Bertsch

Brandon P. van Zyl, E. Zaremba, Joseph Towers

The collective excitations of a zero-temperature, spin-polarized, harmonically trapped, two-dimensional dipolar Fermi gas are examined within the Thomas-Fermi--von Weizs\"acker hydrodynamic theory. We focus on repulsive interactions and investigate the dependence of the excitation frequencies on the strength of the dipolar interaction and particle number. We find that the mode spectrum can be classified according to bulk modes, whose frequencies are shifted upward as the interaction strength is increased, and an infinite ladder of surface modes, whose frequencies are independent of the interactions in the large particle limit. We argue quite generally that it is the local character of the two-dimensional energy density that is responsible for the insensitivity of surface excitations to the dipolar interaction strength and not the precise form of the equation of state. This property will not be found for the collective excitations of harmonically trapped, dipolar Fermi gases in one and three dimensions, where the energy density is manifestly nonlocal.

I. A. Fomin

Arkady Shekhter, Chandra Mohan Varma

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.