Chapter 8: Collective Modes

Collective excitations are simple but very informative probes in all types of physical systems. They are particularly useful for the characterization of plasmas on large distance and long timescales. The studies of collective modes in plasmas are invaluable in fundamental research but also very useful for practical applications. Examples of various forms of plasmas include ionized gases, interstellar and intergalactic media, electron plasmas in solids, relativistic plasmas in heavy-ion collisions and the early Universe, as well as degenerate states of dense matter in compact stars. While chiral electron plasmas in Dirac and Weyl semimetals share many common properties with other plasmas, they do have a number of unusual features. Since electrons are electrically charged, collective modes of the corresponding plasma are accompanied by oscillating electromagnetic fields. Various types of such modes in chiral electron plasmas of Dirac and Weyl semimetals will be considered in this chapter. For simplicity, however, only waves with small amplitudes described by linearized equations will be presented. In the opposite regime of large amplitude waves, a diverse range of nonlinear phenomena can also be realized in a chiral matter. While this is also a fascinating topic, it has not been studied much in the literature yet and will not be covered here…