Nonlinear Optical Response in Graphene/WX₂ (X = S, Se, and Te) van der Waals Heterostructures

Light-frequency conversion based on two-dimensional (2D) materials is of great importance for modern nano- and integrated photonics. Herein, we report both the intrinsic (from the pure WX₂ (X = S, Se, and Te)) and extrinsic (from the interface of graphene/WX₂) second-order nonlinear coefficient tensor from graphene/WX₂ van der Waals (vdW) heterostructures by first-principles calculations. The prominent peaks in the dispersion relation of the intrinsic second-order nonlinear coefficient in monolayer WX₂ are due to the Van Hove singularity in the high-symmetry point or along the high-symmetry line with high joint density of states. The enhanced nonlinear optical response in the infrared band can be achieved in graphene/WS₂ vdW heterostructures, resulting from the interlayer charge transfer between graphene and WS₂. The value of the intrinsic second-order nonlinear coefficients of graphene/WSe₂ vdW heterostructures is 1.5 times larger than that of pure monolayer WSe₂ at the band gap energy of monolayer WSe₂ because of the enhanced carrier generation after the heterostructure formation. Different from pure monolayer WX₂, azimuthal angle-dependent second harmonic generation from graphene/WX₂ vdW heterostructures exhibits extraordinary rotational symmetry at different photon energies, which can be used to deduce the extrinsic second-order nonlinear coefficient. These results pave the way for the nonlinear optical coefficient design based on 2D heterostructures for nonlinear nanophotonics and integrated devices.