Effective Floquet Hamiltonians for periodically driven twisted bilayer graphene

Abstract

We derive effective Floquet Hamiltonians for twisted bilayer graphene driven by circularly polarized light in two different regimes beyond the weak-drive, high-frequency regime. First, we consider a driving protocol relevant for experiments with frequencies smaller than the bandwidth and weak amplitudes and derive an effective Hamiltonian, which through a symmetry analysis, provides analytical insight into the rich effects of the drive. We find that circularly polarized light at low frequencies can selectively decrease the strength of AA-type interlayer hopping while leaving the AB-type unaffected. Then, we consider the intermediate frequency and intermediate-strength drive regime. We provide a compact and accurate effective Hamiltonian which we compare with the Van Vleck expansion and demonstrate that it provides a significantly improved representation of the exact quasienergies. Finally, we discuss the effect of the drive on the symmetries, Fermi velocity, and the gap of the Floquet flat bands.