Excitonic response of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>AA</mml:mi></mml:mrow><mml:mo>′</mml:mo></mml:msup></mml:math> and AB stacked hBN bilayers
J. C. G. Henriques, Bruno Amorim, R. M. Ribeiro, N. M. R. Peres
Abstract
In this paper, we discuss the optical response due to the excitonic effect of two types of hBN bilayers: AB and ${\mathrm{AA}}^{\ensuremath{'}}$. Understanding the properties of these bilayers is of great utility to the study of twisted bilayers at arbitrary angles since these two configurations correspond to the limit cases of ${0}^{\ensuremath{\circ}}$ and ${60}^{\ensuremath{\circ}}$ rotation. To obtain the excitonic response, we present a method to solve a four-band Bethe-Salpeter equation by casting it into a one-dimensional problem, thus greatly reducing the numerical burden of the calculation when compared with strictly two-dimensional methods. We find results in good agreement with ab initio calculations already published in the literature for the ${\mathrm{AA}}^{\ensuremath{'}}$ bilayer, and predict the excitonic conductivity of the AB bilayer, which remains largely unstudied. The main difference in the conductivity of these two types of bilayers is the appearance of a small, yet well-resolved resonance between two larger ones in the AB configuration. This resonance is due to a mainly interlayer exciton, and is absent in the ${\mathrm{AA}}^{\ensuremath{'}}$ bilayer. Also, the conductivity of the AB bilayer is due to both intralayer and interlayer excitons and is dominated by $p$-states, while intralayer $s$-states are the relevant ones for the ${\mathrm{AA}}^{\ensuremath{'}}$ configuration, like in a monolayer. The effect of introducing a bias in the ${\mathrm{AA}}^{\ensuremath{'}}$ bilayer is also discussed.