Moiré induced topology and flat bands in twisted bilayer WSe2 : A first-principles study

Abstract

We study the influence of strong spin-orbit interaction on the formation of flat bands in relaxed twisted bilayer $\mathrm{W}{\mathrm{Se}}_{2}$. Flat bands, well separated in energy, emerge at the band edges for twist angles $\ensuremath{\theta}$ near ${0}^{\ensuremath{\circ}}$ and ${60}^{\ensuremath{\circ}}$. For $\ensuremath{\theta}$ near ${0}^{\ensuremath{\circ}}$, the interlayer hybridization together with a moir\'e potential determines the electronic structure. The bands near the valence band edge have nontrivial topology, with Chern numbers equal to $+1$ or $\ensuremath{-}1$. We propose that the nontrivial topology of the first band can be probed experimentally for twist angles less than a critical angle of $3.5{}^{\ensuremath{\circ}}$. For $\ensuremath{\theta}$ near ${60}^{\ensuremath{\circ}}$, 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 wave functions for both ranges of $\ensuremath{\theta}$ match well with recent experimental observations.