Analytic model of energy spectrum and absorption spectra of bilayer graphene

Abstract

A model to obtain the analytical form of energy spectrum and eigenvectors of the Beranl bilayer graphene, with all the tight-binding parameters included, is proposed. The bonding and anti-bonding states, linked together by a coupling term, are not completely decoupled through the chosen symmetrized wave functions. We show that such a coupling term, originating from the tight-binding parameter γ3, can be neglected and that the decoupled bonding and anti-bonding states are, respectively, described by a 2×2 matrix. The analytical energy spectrum and eigenvectors are obtained and applied to express the optical dipole matrix in a closed form, which determines the feature of optical absorption spectra. Four possible interband transitions, causing four sub-spectra, at zero temperature are allowed at chemical potential μ=0. The fine structures of total absorption spectra result form the superposition of four sub-spectra. Most importantly, comparison with the AA-stacking bilayer graphene exhibits that the energy spectra, eigenstates, and optical properties are strongly dependent on the stacking ordering.