Second harmonic generation control in twisted bilayers of transition metal dichalcogenides

The twist angle in transition metal dichalcogenide heterobilayers is a compelling degree of freedom that determines electron correlations and the period of lateral confinement of moir\'e excitons. Here we perform polarization-resolved second harmonic generation (SHG) spectroscopy of $\mathrm{Mo}{\mathrm{S}}_{2}/\mathrm{W}{\mathrm{Se}}_{2}$ heterostructures. We demonstrate that by choosing suitable laser energies the twist angle between two monolayers can be measured directly on the assembled heterostructure. We show that the amplitude and polarization of the SHG signal from the heterostructure are determined by the twist angle between the layers and exciton resonances at the SH energy. For heterostructures with close to zero twist angle, we observe changes of exciton resonance energies and the appearance of new resonances in the linear and nonlinear susceptibilities.