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Emergence of flat bands in the quasicrystal limit of boron nitride twisted bilayers

Lorenzo SponzaVan Binh VuElisa Serrano RichaudHakim AmaraSylvain Latil
Nov 2023
We investigate the electronic structure and the optical absorption onset of hexagonal boron nitride bilayers with twist angles in the vicinity of 30$^\circ$. Our study is carried out with a tight-binding model that we developed on purpose and validated against DFT simulations. We demonstrate that approaching 30$^\circ$ (quasicrystal limit), all bilayers sharing the same moir\'e supercell develop identical band structures, irrespective of their stacking sequence. This band structure features a bundle of flat bands laying slightly above the bottom conduction state which is responsible for an intense peak at the onset of independent-particle absorption spectra. These results reveal the presence of strong, stable and stacking-independent optical properties in boron nitride 30$^\circ$-twisted bilayers. By carefully analyzing the electronic spatial distribution, we elucidate the origin of these states as due to interlayer B-B coupling. We take advantage of the the physical transparency of the tight-binding parameters to derive a simple triangular model based on the B sublattice that accurately describes the emergence of the bundle. Being our conclusions very general, we predict that a similar bundle should emerge in other close-to-30$^\circ$ bilayers, like transition metal dichalcogenides, shedding new light on the unique potential of 2D materials.
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