Floquet topological flat bands and Landau Levels in two-dimensional systems

Flat electronic bands and Landau levels in equilibrium condensed matter systems have been common avenues 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 and Landau levels with nontrivial topology in 2D or quasi-2D systems subject to circularly-polarized light. The Floquet flat bands and Landau levels 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.