Effect of Spin-orbit Coupling in Twisted Bilayer and Double Bilayer Transition Metal Dichalcogenides*

Since the discovery of flat bands at magic angles in twisted bilayer graphene, the formation of flat bands has been predicted for several other twisted bilayers, especially twisted transition metal dichalcogenides (TMDs). The effect of spin-orbit coupling is quite prominent in TMDs such as WSe₂. Using a multiscale approach, based on classical force-fields for structural relaxation and density functional theory calculations for electronic structure, we investigate the influence of spin-orbit coupling on the flat bands in twisted TMD systems. Owing to spin-valley coupling, spin-orbit interaction affects the flat bands of the twisted bilayer TMDs with twist angle close to 0^o differently than those near 60^o. The spin-orbit splitting of bands near valence band edge decreases with smaller twist angle. We study wavefunction localization near valence and conduction band edges in these bilayers and extend our studies to twisted double bilayer TMDs as well.