We have examined the electronic structure of twisted bilayers of ${\mathrm{WSe}}_2$ within ab initio electronic structure calculations. Flat bands are found to emerge above a set of dispersing bands at a twist angle of $3.48{}^{\circ }$, whereas they are absent at $19.03{}^{\circ }$ which has a similar-sized moiré cell. The presence of the flat bands at the valence-band maximum are traced to the strong perturbations from zone-boundary scattering found for small angles. This follows from the fact that the strongest Fourier components of the lattice potential are associated with the primitive cell vectors, justifying a description of the electronic structure as a perturbation to the unrotated limit. The layer polarization of the charge density associated with the valence-band maximum also allows for tuning the electronic structure with an electric field, thereby driving a semiconductor-metal-semiconductor transition.

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• Electronic structure
• First-principles calculations
• Transition metal dichalcogenides