▎ 摘　　要

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 Gamma K in the first Brillouin zone. V-g effectively induces the nonzero dipole matrix element along the high symmetry line Gamma K, 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.