Effects of Anisotropy on Magnetoplasma Waves in a Charged Fermi-Liquid System

Abstract

The propagation of the plasma modes in the presence of a static magnetic field and in an electron liquid is studied in terms of the Landau Fermi-liquid theory for a system with an anisotropic Fermi surface. Two types of anisotropy are studied: (a) Weak anisotropy; the resonant frequency of the normal modes is calculated in the long-wavelength limit, $q\to 0$, for a system with a nearly spherical Fermi surface. It is found that the deviation from the isotropic case is of the linear order of the anisotropy. Application to the alkali metals is briefly discussed. Effects of weak anisotropy of the Landau $F$ function is also studied. (b) Strong anisotropy; the dispersion relations of the modes propagating parallel to the magnetic field near the cyclotron frequency ${\omega }_c$ and its harmonics $m{\omega }_c$ are calculated for a system with a simplified Fermi surface which satisfies the Gor'kov-Dzyaloshinskii condition. It is found that, except for the $m=1\mathrm{}$ modes, all higher-$m$ modes have large finite (or infinite) cutoff wave vectors even in the weak coupling limit; while in the isotropic case, all cutoff wave vectors approach zero in the same limit. It is suggested that this simplified model may be relevant to the noble metals.