Kinetic instabilities in bidimensional Dirac materials

Plasmonics in bidimensional materials has proved an active field of study, with these systems showing potential to be used as future optoelectric devices for a number of high-frequency applications. While the hydrodynamic regime is well studied in literature, to go beyond the high-wavelength and local equilibrium regime, a kinetic model is used. To include important quantum corrections to the dynamics of the charge carriers, this model is derived from the Schrödinger equation via the Wigner quasidistribution function in a mean field approach.

A numerical simulation code is developed, which can simulate kinetic systems with wide generality, including the effects of quantum statistics, band structures of different materials, and arbitrary interparticle interactions. This code is parallelized for use in large, high-performance simulations. With this model, with the appropriate approximations, as a starting point, as well as the simulations to further study non-linear phenomena, a number of waves and instabilities are described.

In the static-field case, the frequency and lifetime of plasmons is derived, and the behaviour of the bidimensional two-stream instability, which leads to a collisionless anomalous conductivity, is found. We describe the lack of confinement of transverse electromagnetic waves in these materials, but find a related instability which spontaneously generates out-of-plane magnetic fields. Finally, a related zero-frequency clustering instability in a system of repulsive particles is shown.