▎ 摘　　要

A class of integrable models, such as the one-dimensional transverse-field Ising model, responds nonmono-tonically to a periodic drive with respect to the driving parameters and freezes almost absolutely for certain combinations of the latter. In this paper, we go beyond the two-band structure of the Ising-like models studied previously and ask whether such an unusual nonmonotonic response and near-absolute freezing occur in integrable systems with a higher number of bands. To this end, we consider a tight-binding model for bilayer graphene subjected to an interlayer potential difference. We find that when the potential is driven periodically, the system responds nonmonotonically to variations in the driving amplitude V0 and frequency omega and shows near-absolute freezing for certain values of V0/omega. However, the freezing occurs only in the presence of a constant bias in the driving, i.e., when V = V' + V0 cos omega t. When V' = 0, the freezing is switched off for all values of V0/omega. We support our numerical results with analytical calculations based on a rotating wave approximation. We also give a proposal to realize the driven bilayer system via ultracold atoms in an optical lattice, where the driving can be implemented by shaking the lattice.