We study the influence of strong spin-orbit interaction on the formation of flat bands in relaxed twisted bilayer WSe$_2$. Flat bands, well separated in energy, emerge at the band edges for twist angles ($theta$) close to 0$^o$ and 60$^o$. For $theta$ close to 0$^o$, the interlayer hybridization together with a moir{e} potential determines the electronic structure. The bands near the valence band edge have non-trivial topology, with Chern numbers equal to +1 or $-$1. We propose that this can be probed experimentally for twist angles less than a critical angle of 3.5$^o$. For $theta$ near 60$^o$, the flattening of the bands arising from the K point of the unit cell Brillouin zone is a result of atomic rearrangements in the individual layers. Our findings on the flat bands and the localization of their wavefunctions for both ranges of $theta$ match well with recent experimental observations [1,2].
Download