Determination of Twist Angle in Hetero-Bilayer TMDs with Phase-Resolved Second-Harmonic Generation

 Second-harmonic generation (SHG) is a non-linear optical process in which a non-centrosymmetric optical medium interacts with two identical photons to generate another with a doubled frequency. Whereas SHG has been widely used in determining the orientation of various 2D single crystals, it has yet to prove to be applicable to artificially stacked heterocrystals. In this work, we show that the twist angle and orientation of individual layers of hetero-bilayer transition metal dichalcogenides (TMDs) can be directly measured by phase-resolved SHG spectroscopy and imaging. For a complete wave description of SHG signals, the phase and intensity were obtained by spectral phase interferometry for two orthogonally polarized components. For MoS₂/WS₂ bilayers with negligible interlayer coupling, their twist angle could be determined from the polarized interferometric data and spatially mapped in a raster scanning mode. On the contrary, MoSe₂/WS₂ bilayers exhibited significant deviation in SHG intensity and phase from what was expected from non-interacting bilayers, and the deviation of each layer could be determined respectively from the data. We will discuss possible causes for these unexpected deviations in SHG behavior.