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

TL;DR

This paper investigates how twisting bilayer hBN affects its electronic structure, charge distribution, and polarization, revealing flat bands and the influence of lattice relaxation and alignment.

Contribution

It introduces a detailed analysis of flat bands in twisted bilayer hBN, including effects of lattice relaxation and polarization, with continuum models explaining the spectrum.

Findings

Flat bands appear in twisted bilayer hBN, with spectrum independence at small angles after relaxation.

Spontaneous polarization occurs only in parallel alignment, indicating large interlayer hopping.

Lattice relaxation significantly alters the electronic spectrum and charge distribution.

Abstract

We study the effect of twisting on bilayer graphene. The effect of lattice relaxation is included; we look at the electronic structure, piezo-electric charges and spontaneous polarisation. 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 study appropriate continuum models, at the same time explaining the spectrum We find that even though the spectra for both parallel an anti-parallel alignment are very similar, the spontaneous polarisation effects only occur for parallel alignment. We argue that this suggests a large interlayer hopping between boron and nitrogen.