Excitonic Absorption Signatures of Twisted Bilayer WSe$_{2}$ by Electron Energy-Loss Spectroscopy

Moir\'{e} twist angle underpins the interlayer interaction of excitons in twisted van der Waals hetero- and homo-structures. The influence of twist angle on the excitonic absorption of twisted bilayer tungsten diselenide (WSe$_{2}$) has been investigated using electron energy-loss spectroscopy. Atomic-resolution imaging by scanning transmission electron microscopy was used to determine key structural parameters, including the nanoscale measurement of the relative twist angle and stacking order. Detailed spectral analysis revealed a pronounced blueshift in the high-energy excitonic peak C with increasing twist angle, up to 200 meV when compared to the AA$^{\prime}$ stacking. The experimental findings have been discussed relative to first-principle calculations of the dielectric response of the AA$^{\prime}$ stacked bilayer WSe$_{2}$ as compared to monolayer WSe$_{2}$ by employing the \textit{GW} plus Bethe-Salpeter equation (BSE) approaches, resolving the origin of higher energy spectral features from ensembles of excitonic transitions, and thus any discrepancies between previous calculations. Furthermore, the electronic structure of moir\'{e} supercells spanning twist angles of $\sim$9.5-46.5$^{\circ}$ calculated by density functional theory (DFT) were unfolded, showing an uplifting of the conduction band minimum near the $Q$ point and minimal change in the upper valence band concurrently. The combined experiment/theory investigation provides valuable insight into the physical origins of high-energy absorption resonances in twisted bilayers, which enables to track the evolution of interlayer coupling from tuning of the exciton C transitions by absorption spectroscopy.