Abstract
The optical conductivity of graphene monolayer and multilayers are theoretically studied taking into account of the full dispersion, yielding results that are valid up to the ultraviolet region. Compared to the optical conductivity of monolayer graphene, extra peak structures appear in both the infrared and ultraviolet frequency regions for the multilayer case, which is understood as a combined effect of van Hove singularities in the energy band structures and optical transition selection rules. The number of ultraviolet peaks is equal to the number of layers. The number of infrared peaks in an even-layered graphene is equal to one half of the layer number. In odd-layered graphene, due to the existence of a monolayer-like subband, the number of infrared peaks is equal to that in the corresponding even-layered graphene with one layer less.
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