We study the effect of twisting on bilayer $h\text{−}\mathrm{BN}$. The effect of lattice relaxation is included; we look at the electronic structure, piezoelectric charges, and spontaneous polarization. We show that the electronic structure without lattice relaxation shows a set of extremely flat in-gap states similar to Landau levels, where the spacing scales with twist angle. With lattice relaxation we still have flat bands, but now the spectrum becomes independent of twist angle for sufficiently small angles. We describe in detail the nature of the bands and we study appropriate continuum models, at the same time explaining the structure of the in-gap states. We find that even though the spectra for both parallel and antiparallel alignment are very similar, the spontaneous polarization effects only occur for parallel alignment. We argue that this suggests a large interlayer hopping between boron and nitrogen.

• Received 4 December 2020
• Revised 4 March 2021
• Accepted 16 March 2021

DOI:https://doi.org/10.1103/PhysRevB.103.125427