An analytical approach for the energy spectrum and optical properties of gated bilayer graphene

Abstract

First, we present an analytical approach to access the exact energy spectrum and wave functions of gated Bernal bilayer graphene (BBLG), with all the tight-binding parameters included. To tackle the broken mirror symmetry caused by a gated voltage (V_g) and interlayer interactions, we create a unitary transformation to reduce the Hamiltonian matrix of BBLG to a simple form, which can offer the analytical energy spectrum. The formulae generate the gated tunable energy bands and reveal that V_g changes the subband spacing, produces the oscillating bands, and increases the band-edge states. Then, we employ the analytical model to revisit the optical dipole matrix element and optical absorption spectra. In the absence of V_g, the anisotropic dipole matrix element exhibits a maximum around the point M and zero value along the high symmetry line ΓK in the first Brillouin zone. V_g effectively induces the nonzero dipole matrix element along the high symmetry line ΓK, which makes a significant contribution in the absorption spectra. Moreover, the application of V_g opens an optical gap and gives rise to a profound low-energy peak in the absorption spectra. The dependence upon the gated bias V_g for the location and height of this peak clearly emerges through the analytical model. Our exact analytical model can be further used to study the many-body effect and exciton effect on the electronic and optical properties of BBLG.