Crystal-Momentum-Resolved Contributions to Harmonics in Laser-Driven Graphene

We investigate the crystal-momentum-resolved contributions to high-order harmonic generation in laser-driven graphene by semi-conductor Bloch equations in the velocity gauge. It is shown that each harmonic is generated by electrons with the specific initial crystal momentum. The higher harmonics are primarily contributed by the electrons of larger initial crystal momentum because they possess larger instantaneous energies during the intra-band motion. Particularly, we observe circular interference fringes in the crystal-momentum-resolved harmonics spectrum, which result from the inter-cycle interference of harmonic generation. These circular fringes will disappear if the inter-cycle interference is disrupted by the strong dephasing effect. Our findings can help to better analyze the mechanism of high harmonics in graphene.