Floquet topological flat bands in two-dimensional systems

Flat electronic bands in equilibrium condensed matter systems have been a common avenue to nontrivial correlation effects, with the twisted bilayer graphene being a most recent prominent example. It is expected that flat quasienergy bands can also enhance interaction effects in time-periodic Floquet systems and may lead to novel interaction driven metastable phases. Here, we propose a general approach to realizing Floquet flat bands with nontrivial topology in 2D or quasi-2D systems subject to circularly-polarized light. By using a simple model that can interpolate between Schrödinger and Dirac electrons, we demonstrate their different band flattening behaviors within Floquet theory. The flat band condition, determined by the ratio between the time-periodic electric field strength and its frequency, can be qualitatively obtained from perturbation theory. Moreover, flat bands argued in this work can be realized without the need of fine tuning in contrast to twisted bilayer graphene. Our proposal may pave the way to novel interaction-driven phases in nonequilibrium systems.