Eﬀective Floquet Hamiltonians for periodically-driven twisted bilayer graphene
We derive eﬀective Floquet Hamiltonians for twisted bilayer graphene driven by circularly polar- ized 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 an- alytical 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.