Monolayer graphene placed with a twist on top of AB-stacked bilayer graphene hosts topological flat bands in a wide range of twist angles. The dispersion of these bands and gaps between them can be efficiently controlled by a perpendicular electric f
ield, which induces topological transitions accompanied by changes of the Chern numbers. In the regime where the applied electric field induces gaps between the flat bands, we find a relatively uniform distribution of the Berry curvature. Consequently, interaction-induced valley- and/or spin-polarized states at integer filling factors are energetically favorable. In particular, we predict a quantum anomalous Hall state at filling factor $ u=1$ for a range of twist angles $1^circ<theta <1.4^circ$. Furthermore, to characterize the response of the system to magnetic field, we computed the Hofstadter butterfly and the Wannier plot, which can be used to probe the dispersion and topology of the flat bands in this material.
Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as useful experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective Hamiltonians with ph
ysics potentially quite distinct from short-range systems can be realized. In this Letter, we derive general bounds on the linear response energy absorption rates of periodically driven systems of spins or fermions with long-range interactions that are sign changing and fall off as $1/r^alpha$ with $alpha > d/2$. We show that the disordered averaged energy absorption rate at high temperature decays exponentially with the driving frequency. This strongly suggests the presence of a prethermal plateau in which dynamics is governed by an effective, static Hamiltonian for long times, and we provide numerical evidence to support such a statement. Our results are relevant for understanding timescales of both heating and hence new dynamical regimes described by effective Hamiltonians in such long-range systems.
