Angular dependence of the velocity of sound in semimetals

Abstract

A wide range of phenomena of the electromagnetic generation of sound in metals in a magnetic field is reviewed. All phenomena of mutual conversion of waves and of sound generation are due to the interaction of conduction electrons with phonons. A wide variety of resonance effects in a magnetic field determines numerous mechanisms for direct sound generation by an external microwave.The basic equations and boundary conditions for the problem of electron-phonon interaction in metals are presented in the quasiclassical approximation. In the low-temperature region under the conditions of the anomalous skin effect the wave conversion is caused, besides by inductive interaction, also by electron-phonon interaction via the deformation potential. The major conversion mechanism of an electromagnetic wave into sound results in various resonance effects in a magnetic field in conditions of strong spatial dispersion. We present an exact solution of the problem for an alkali metal in a magnetic field normal to the surface. We analyze the asymptotic approximations related with the skin-effect anomaly, the coupling of electromagnetic and acoustic waves in metals, and the role of surface scattering. We study the effect of resonance renormalization of electron-phonon interaction in metals with a complex dispersion law, which results in a partial compensation of resonance singularities and appears in Doppler-shifted cyclotron resonances. The doppleron-phonon resonance and its polarization effects are investigated.The electromagnetic generation of sound in metals in a magnetic field parallel to the surface is due to the additional mechanism of selecting “effective” electrons, where resonance effects are observed. We study geometric and cyclotron resonances, and the resonance coupling of a sound wave with a cyclotron wave. The amplitude and phase of the generated sound depend on the character of electron scattering on the metal boundary because in specular scattering a group of surface electrons move in the skin layer and get reflected many times from the separation boundary.The tilt effect in electron-phonon interaction appears during the electromagnetic generation of sound as strong peculiarities of the sound amplitude in terms of the tilting angle of the magnetic field relative to the surface of the metal. It is caused by an abrupt introduction of the mechanism of collisionless resonance interaction of conduction electrons with sound, as the angle between the magnetic field H and the direction of sound wave propagation varies.A new type of sound wave is generated in metals which are placed in a magnetic field under irradiation by a microwave. Besides a conventional wave propagating with sound velocity s0, an improper sound is excited; depending on the magnetic field orientation relative to the metal surface, it propagates with the Fermi electron velocity vF s0 in the case of a perpendicular magnetic field. In a titled magnetic field the improper sound is a standing wave in a semibounded sample, having the form of peaks of the acoustic field, situated at distances multiple of the cyclotron electron diameter. The peak amplitude is (qδ)2 1 times larger than the amplitude of usual sound (q = ω/s0) is the sound wave vector, δ is the thickness of the skin layer). The effect is caused by ballistic transport of energy of an electromagnetic wave from a skin layer to the bulk of the metal by specific electrom groups. The “angular resonance effect” refers to the rapid growth of the improper sound peak amplitude as a function of the tilting angle of the magnetic field relative to the surface.The diamagnetic resonance appears as peculiarities of the electromagnetic signal and improper sound when it passes through a metal plate whose thickness is comparable with the length of the electron mean free path. The resonance lineshape is studied.All the theoretical results are in good agreement with the known experimental data. The conversion of an electromagnetic wave into sound has become widely applicable to various techniques aimed at studying the electro-acoustic properties of metals, and provides the basis of a new method, the “hybrid spectroscopy of metals”.