Nonlinear optical response of Twisted Bilayer graphene

In recent years the interest on graphene based Moire systems has spiked due to discovery of high temperature superconductivity for specific twisting angles. The nonlinear response of such systems to ultra-short pulses, however also represents a very promising field due to the possibility of engineering optical properties through twisting. We characterise the nonlinear optical current spectrum of twisted bilayer graphene in the kp approximation, for different twisting angles. We do this by using the Dirac-Bloch equations (DBEs), a non perturbative version of the semiconductor Bloch equations. The DBEs, used for the first time in 2010 by Ishikawa to study the optical properties of graphene are a powerful tool as they allow to obtain both the interband and intraband optical response relatively easily. We investigate the generation of high harmonics and the emergence of even harmonics when the Moire-bands low energy Hamiltonian breaks the inversion symmetry. In particular we analyse the behaviour of the nonlinear current when flat bands appear which is expected to change quite dramatically due to Berry curvature hotspots and reduced quasiparticle velocities.