We calculate the finite-frequency conductivity of bilayer graphene with a relative twist between the layers. The low frequency response at zero doping shows a flat conductivity with value twice that of the monolayer case and at higher frequency a strong absorption peak occurs. For finite doping, the low frequency flat absorption is modified into a peak about zero frequency (the Drude response) accompanied by an interband edge which results from the transfer of spectral weight from interband to intraband absorption due to Pauli blocking. If the system is doped sufficiently such that the chemical potential reaches beyond the low-energy saddle point in the twisted bilayer band structure, a strong low frequency absorption peak appears at an energy related to an effective interlayer hopping energy, which may be used to identify this parameter and confirm the existence of the saddle point which gives rise to a low energy van Hove singularity in the electronic density of states.

Accepted in Phys. Rev. B Rapid Communications