Interlayer coupling effect in high-order harmonic generation of the phosphorene/graphene heterostructure

Heterostructures introduce additional degrees of freedom to two-dimensional materials, providing an alternative way to manipulate solid high-order harmonic generation (HHG). However, the impact of interlayer coupling on the HHG of heterostructures remains unexplored. Taking the phosphorene/graphene heterostructure as an example, we theoretically investigate the interlayer coupling effect in the HHG of heterostructures by solving the semiconductor Bloch equations with the accelerated Bloch-like basis in the Wannier gauge. It is found that there are obvious differences between the high-order harmonics generated by the phosphorene/graphene heterostructure, its monolayers, and the phosphorene/graphene heterostructure without any interlayer couplings. Further study reveals that the lattice strain affects the harmonic yield of the phosphorene/graphene heterostructure, but does not alter the structure of the ellipticity dependence of the harmonic yield. Conversely, the interlayer coupling significantly changes the ellipticity and orientation dependences of the harmonic yield by allowing the transitions between the energy bands of different layers. Moreover, we find that the nearest-neighbor couplings between the specific carbon and phosphorus atoms dominate the overall interlayer coupling. Finally, an all-optical method for retrieving the dephasing time is proposed by means of a one-to-one mapping relationship between the dephasing time and the ellipticity in which the seventh-harmonic yield reaches the maximum. This work provides deeper insight into the HHG mechanism in heterostructures.