Valley-resolved interband excitation and emission in gapped graphene

We theoretically investigate the electronic dynamics in gapped graphene driven by a bicircular field. The results indicate that the residual population on the conduction band is obviously asymmetric in the K and ${\mathrm{K}}^{\ensuremath{'}}$ valleys. Through analyzing the electron trajectory, we find that the interband transitions are determined by the compensation of two phases: the dynamic phase and the full dipole phase (including the transition dipole phase and the Berry phase). When the rates of change of the dynamic phase and the full dipole phase nearby the ionization time have the inverse signs, the unidirectional interband transition from the valence band (VB) to the conduction band (CB) results in the constructive interference of the population. In contrast, when they have the same signs, the bidirectional transition (CB$\ensuremath{\rightarrow}$VB and VB$\ensuremath{\rightarrow}$CB) results in the destructive interference. The constructive interference and the destructive interference lead to the asymmetric distribution of the CB population. Moreover, we also investigate the harmonic emission and find that only the $3n+2$ harmonics are generated in the cutoff region. This phenomenon can be attributed to the asymmetric distribution of the CB population and the trefoil vector potential of the electric field. Due to the dependence on population distribution, the harmonics can be a promising optical way to detect the valley excitation of the gapped graphene.