Theory of high-order harmonic generation for gapless graphene

Abstract

We study the high-harmonic spectrum emitted by a single-layer graphene, irradiated by an ultrashort intense infrared laser pulse. We show the emergence of the typical non-perturbative spectral features, harmonic plateau and cut-off, for mid-infrared driving fields, at fluences below the damage threshold. In contrast to previous works, using THz drivings, we demonstrate that the harmonic cut-off frequency saturates with the intensity. Our results are derived from the numerical integration of the time-dependent Schrödinger equation using a nearest neighbor tight-binding description of graphene. We also develop a saddle-point analysis that reveals a mechanism for harmonic emission in graphene different from that reported in atoms, molecules and finite gap solids. In graphene, the first step is initiated by the non-diabatic crossing of the valence band electron trajectories through the Dirac points, instead of tunneling ionization/excitation. We include a complete identification of the trajectories contributing to any particular high harmonic and reproduce the harmonic cut-off scaling with the driving intensity.