Photon absorption in twisted bilayer graphene

We investigate one- and two-photon absorption in twisted bilayer graphene (TBLG) by examining the effects of tuning the twist angle $\ensuremath{\theta}$ and the excitation energy ${E}_{l}$ on its absorption coefficients ${\ensuremath{\alpha}}_{i=1,2}$. We find that ${\ensuremath{\alpha}}_{1}$ as a function of ${E}_{l}$ for TBLG exhibits distinct peaks corresponding to its van Hove singularities. For small twist angles, such as $\ensuremath{\theta}\ensuremath{\sim}1.{8}^{\ensuremath{\circ}}$, the magnitude of the resonant peak for ${\ensuremath{\alpha}}_{1}$ is roughly twice that of bilayer graphene (BLG). This enhanced response, compared to BLG, can be attributed to the increased density of states in the twisted structure. However, as the twist angle increases, the magnitude of the resonant peak approaches that of two decoupled single-layer graphene (SLG) sheets. On the other hand, the two-photon absorption coefficient ${\ensuremath{\alpha}}_{2}$ for TBLG at low twist angles displays an enhancement of about one order of magnitude compared to SLG at the energies corresponding to the resonant peak, as well as a small but notable increase relative to BLG. As the twist angle decreases from ${8}^{\ensuremath{\circ}}$ to $2.{5}^{\ensuremath{\circ}}$, the resonant peak intensifies by three orders of magnitude. Interestingly, as $\ensuremath{\theta}$ increases, the resonant features exhibited by ${\ensuremath{\alpha}}_{i=1,2}$ vs ${E}_{l}$ shift progressively from the infrared to the visible. On doping TBLG, both ${\ensuremath{\alpha}}_{1}$ and ${\ensuremath{\alpha}}_{2}$ vs ${E}_{l}$ remain essentially unchanged, but with a slight redshift in their resonant peaks. Additionally, we explore various polarization configurations for two-photon absorption and determine the conditions under which ${\ensuremath{\alpha}}_{2}$ becomes extremal.