Nonlinear response of bilayer graphene at terahertz frequencies

A density-matrix formalism within the length gauge is developed for the purpose of calculating the nonlinear response of intrinsic bilayer graphene at terahertz frequencies. Employing a tight-binding model, we find that the interplay between the interband and intraband dynamics leads to strong harmonic generation at moderate field amplitudes. Specifically, we find that at low temperature (10 K), the reflected field of undoped suspended bilayer graphene exhibits a third harmonic amplitude that is 0.06% of the fundamental of the incident field, which corresponds to 30% of the fundamental in the reflected field for an incident 1-THz single-cycle pulse with a field amplitude of 1.5 kV/cm. More interestingly, we find that as the central frequency of the incident field is increased, the third harmonic amplitude also increases; reaching a maximum of 53% of the fundamental in the reflected field (0.11% of the fundamental in the incident field) for an incident frequency of 2 THz and amplitude of 2.5 kV/cm.