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

TL;DR

This paper derives adiabatic solutions to the Dirac equation for graphinos in intense electromagnetic fields, predicting high-order harmonic emissions with specific spectral features near Dirac points, relevant for non-perturbative laser interactions.

Contribution

It provides the first analytic adiabatic solutions for massless Dirac particles in intense fields, enabling non-perturbative analysis of harmonic generation in graphene-like systems.

Findings

High-order harmonics are emitted with relatively stable intensity up to the 81st harmonic.

Spectral features include revival phenomena and plateau formation.

Comparison with 2D graphene shows a sharp harmonic cutoff at a specific order.

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.