Properties of the optical response of the twisted bilayer graphene

In this paper we explore the properties of optical conductivity of twisted bilayer graphene (TBG) for small twist angles based on the continuum model. It is found that the spectrum structure of optical conductivity exhibits the characteristic of the "redshift"with the reduction of twist angle. The redshift of the spectrum structure for TBG can be understood and analyzed with a picture of an effective quantum well with the variable well width. There arises a quasi plateau for the conductivity in the low frequency range the height of which descends as the twist angle reduces. We present a quantitative explanation which is based on the linear dispersion of the connected Dirac cones and the Kubo formula. It is also demonstrated that the quasi plateau can be destroyed due to the Pauli blocking when the Fermi energy moves up away from the neutrality point. Moreover, we find that the van Hove singularities (VHS's) which possess the geometry of the saddle surface do not cause the peak for the interband conductivity at the neutrality point, which is supposed to originates from the negative Gaussian curvature and the symmetry of the local surface of energy band around VHS's.