Adiabatic solution of Dirac equation of "graphinos" in an intense electromagnetic field and emission of high order harmonics near the Dirac points

Abstract

We obtain a class of adiabatic solutions of Dirac equation for the charged massless relativistic quasi-particles that arise from the low-energy excitations \cite{foot-1} in a 2D graphene sheet, interacting with an electromagnetic field. The analytic solutions obtained are useful for {\it non-perturbative} investigation of processes in intense laser fields. As a first example we employ them to predict copious emissions of high order harmonics by THz lasers interacting with the occupied states of graphinos in the vicinity of the degenerate Dirac points. The relative intensity of the emitted harmonics is seen to decrease by only about two orders of magnitude from the 3rd to the 81st harmonic order, and is characterized by two phenomena of "revival" and "plateau" formation in the middle and the far end of the spectrum calculated. A preliminary comparison is made for harmonic emission from 2D graphene that reveals a qualitatively different spectrum in the latter case showing a sharp cutoff at an order $n_{cutoff} = \frac{\omega_B}{\omega}$ where $\omega_B=eF_0b/\hbar$ is the so-called Bloch frequency.