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 $\theta$ near $0^{\circ }$ and ${60}^{\circ }$. For $\theta$ near $0^{\circ }$, the interlayer hybridization together with a moiré potential determines the electronic structure. The bands near the valence band edge have nontrivial topology, with Chern numbers equal to $+1$ or $-1$. We propose that the nontrivial topology of the first band can be probed experimentally for twist angles less than a critical angle of $3.5{}^{\circ }$. For $\theta$ near ${60}^{\circ }$, 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 $\theta$ match well with recent experimental observations.

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• Electronic structure
• Spin-orbit coupling
• Topological phases of matter
• Transition metal dichalcogenides
• Density functional theory