Non-linear conductivity and magnetoplasma waves in compensated metals and semi-metals

Abstract

The existence of non-linear magnetoplasma waves in compensated metals and semi-metals in the presence of a strong magnetic field is predicted. Non-linearity in the case considered is caused by the influence of the magnetic field of the wave on the dynamics of the electrons and holes. The conductivity tensor is calculated neglecting the spatial dispersion and is shown to be in the non-linear regime a differential - with respect to time - operator which is a manifestation of the temporal dispersion effects. The shape of the wave solution obtained is determined by two parameters: the amplitude and the phase velocity V. When the amplitude is small and , where is the Alfvén velocity, the solution transforms into the well-known linear magnetoplasma wave. It is shown that, contrary to the linear case, the non-linear magnetoplasma wave exists when the phase velocity is both less and larger than . It is established that with increase of the velocity and the amplitude being fixed the quasiharmonic wave turns into a series of pulses, the interval between which is growing infinitely. In the aperiodic limit the wave becomes a one-parameter soliton. Its velocity is larger than and depends linearly on . With increase of , when V is fixed, the period of the magnetoplasma wave descends and the wave shape becomes a series of sharp spikes. Thus, when we have transition from a linear wave to an anharmonic one, while when we have a transition from a soliton to a sequence of pulses. Both the soliton and the non-linear periodic wave with have no analogues in the linear case. These electromagnetic waves are essentially non-linear even at small - in comparison with the external magnetic field - amplitudes.

Anomalous galvanomagnetism, cyclotron resonance, and microwave spectroscopy of topological insulators

“…Moreover, this conclusion remains valid in the nonlinear electrodynamics where the dependence of the bulk conductivity on the magnetic field of the current (or of an external EM wave) is taken into account. 24 However, according to Eq. ( 9) the nonzero surface conductivity generates an additional Hall field ∝ σ H /dΣ that affects the cyclotron drift in the direction of the current.…”

The nonlinear effect of transport current on the response of metals to electromagnetic radiation

“…Therefore, spiral waves with large amplitudes can propagate under conditions where the linear electromagnetic excitations vanish [8]. Magnetoplasma shock waves [9] and soliton-like excitations [10] are also predicted for the regime of strong magnetodynamic nonlinearity.…”