Precise Twist Angle Determination in twisted WSe2 via Optical Moiré Phonons

Abstract: Twisted bilayers of transition metal dichalcogenides (TMDC) form moiré superlattices resulting in moiré minibands in momentum space and hosting localized excitons in real space. While moiré superlattices provide access to Mott-Hubbard physics, their energy potential landscape and electronic correlations are highly sensitive to fluctuations of the twist angle, disorder and lattice reconstructions. However, fast and non-invasive experimental access to local twist angle and its spatial variations is challenging. Here, we systematically correlate twist angle variations of twisted WSe2 bilayers across micrometer length scales using a combined lateral force microscopy (LFM) and a micro- Raman spectroscopy approach. These measurements uncover lateral variations in the twist angle by more than 1° across length scales relevant to optical and transport measurements. We demonstrate that twist angles in the range of 3° < $α$ < 12° show distinct Raman response from scattering on optical moiré phonons allowing twist angle determination with high precision and sub-micrometer spatial resolution under ambient conditions. These modes are particularly sensitive in the low-angle twist regime, predicted to host emergent quantum phases. Our results establish micro-Raman spectroscopy of optical moiré phonons as a rapid, non-invasive probe to determine twist angle and to screen local twist angle variations with a precision better than $\pm$ 0.3° and a lateral resolution below one micrometer. This methodology is also applicable to fully hBN-encapsulated heterostructures.