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We study the effect of twisting on bilayer graphene. The effect of latticerelaxation is included; we look at the electronic structure, piezo-electriccharges and spontaneous polarisation. We show that the electronic structurewithout lattice relaxation shows a set of extremely flat in-gap states similarto Landau-levels, where the spacing scales with twist angle. With latticerelaxation we still have flat bands, but now the spectrum becomes independentof twist angle for sufficiently small angles. We describe in detail the natureof the bands, and study appropriate continuum models, at the same timeexplaining the spectrum We find that even though the spectra for both parallelan anti-parallel alignment are very similar, the spontaneous polarisationeffects only occur for parallel alignment. We argue that this suggests a largeinterlayer hopping between boron and nitrogen.

Flat bands, strains, and charge distribution in twisted-bilayer hBN