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.

Floquet engineering of twisted double bilayer graphene

“…In the intermediate-frequency and intermediate drive strength regime, we obtain an effective Hamiltonian by performing a modified rotating frame transformation [59] and taking an average over one period (see Appendix A for details). For our analytical results, we neglect the effect of next-to-nearest neighbor hopping within each bilayer unit (γ 3 = γ 4 = 0), but we will discuss them numerically.…”

“…In the nearinfrared range, several flat bands can be generated [58]. In the low-frequency regime, Floquet drives can generate a large variety of broken symmetry phases as revealed by effective Floquet Hamiltonians [59]. Finally, light confined into a waveguide provides a way to selectively increase or decrease the the magic angle by driving in the low-or high-frequency regime [60].…”

High-order nonlinear optical response of a twisted bilayer graphene

“…One theoretical challenge is that numerous electronic bands are involved in the TBG due to the large unit cell of the moiré structure. Recently, the Floquet band engineering has been proposed based on the tightbinding model [65] and the low-energy effective Hamiltonian involving a few bands [66][67][68]. Another approach is the perturbation theory for the optical field.…”