The anisotropic energy spectrum dependence of the optical conductivity in bilayer graphene

In this paper, the longitudinal optical conductivity in bilayer graphene was calculated analytically and numerically. In addition to the quadratic terms in the effective-mass approximation Hamiltonian, the linear term, which relates to the indirect interlayer coupling, was included. The nonparabolic energy dispersion was obtained. Two intra- and inter-band transition channels for optical transition via carriers absorbing the optical energy are observed. The inter-band transition offers the main contribution and is almost a constant when the optical energy is larger than two times the Fermi energy. In the presence of the complex energy and pseudospin angle relationship, doing the numerical integration to the wavevector k, the contribution of the intra-band optical transition to the optical conductivity (σxxintra(ω)) is strengthened in the low optical energy region, while the analytical results with parabolic energy curves contribute less to σxxintra(ω). In addition, the optical conductivity also depends on the electron density (or gate voltage) and the broadening width.