Doppler-shifted cyclotron resonance in metals

Abstract

The Doppler shift of the frequency of a wave field acting on electrons in a metal can be very large: in the rf range it exceeds the frequency by several orders of magnitude. Therefore, in a dc magnetic field perpendicular to the metal surface the cyclotron resonance is shifted into the frequency range which extends from a few kilohertzs up to a few gigahertz. Unlike the Azbel'-Kaner cyclotron resonance, which is temporal, the Doppler-shifted cyclotron resonance (DSCR) is a spatial resonance. It occurs when the rf wavelength coincides with the extremal displacement of the conduction electrons for one cyclotron period. Owing to Fermi degeneration of the electrons, the DSCR manifests itself as particular components of the electromagnetic field: a doppleron and a Gantmakher-Kaner component. The former is a natural mode of the electromagnetic field in a degenerated plasma of a metal, whose wavelength is close to the extremal displacement of the electrons for a cyclotron period. The latter is also associated with the mentioned electrons, but it is not a natural mode of a plasma. Penetration of the components through a metal slab results in oscillations of the surface impedance of the slab as a function of a dc magnetic field. In this review we present the main results of theoretical and experimental studies of the DSCR in metals carried out during the last three decades. In Part I we describe the properties of dopplerons: their spectra, damping, polarizations, the range of the magnetic field values where they exist, the role of the Fermi surface anisotropy, etc. Part II is devoted to a quantitative description of the excitation of the dopplerons and Gantmakher-Kaner components in metals and to comparison of the theory with experimental data. An important role of the non-specularity of reflection of the conduction electrons from metal surfaces is established. For building the theory, nontrivial methods of solution of the corresponding integrodifferential equations are developed; thus, for example, a method of analytical solution of the two-sided Wiener-Hopf problem is developed. Part III is devoted to nonlinear effects in the DSCR, unexpected for the dense electron plasma in metals. Although the wave field has a little effect on the trajectories of most of the electrons on the Fermi surface, it can significantly alter the motion of the small electron groups responsible for the collisionless wave absorption. When the wave field amplitude is large enough, the electrons are trapped by the field and the collisionless absorption is suppressed. This is valid both for the magnetic Landau damping and for the cyclotron absorption. In the latter case the effect turns out to be so drastic that it results in the appearance of a new doppleron mode which does not exist at small wave field amplitudes. The appearance of the magnetic Landau damping in the case when the wave propagates parallel to a dc magnetic field presents another type of nonlinear effect. It is associated with the fact that the magnetic field of a wave of large amplitude causes the total magnetic field vector to deviate from the wave propagation vector.