Phases of Periodically driven twisted bilayer Transition Metal Dichalcogenide*

Twisted bi-layer materials show many phases, including magnetic, insulating, and superconducting phases. All these phases emerge near the magic angle when the bands are highly flat, and hence the effect of correlation is significant. We propose the "Floquet Engineering" approach to flatten the flat bands in twisted bi-layer transition metal dichalcogenide (tTMD). We show that periodic driving can reduce the flat bandwidth by order of magnitude. This results in the enhancement of the density of states and, eventually, the correlation effect. Further, we study the possibility of broken symmetry phases in periodically driven tTMD. Based on the prior knowledge that non-equilibrium steady-states can be faithfully approximated with the Gibbs state, we perform self-consistent mean-field (SCMF) calculations to study different broken symmetry phases. The SCMF involves the interplay of so-called 'heating' and 'cooling' rates due to the electromagnetic environment, electron-electron interaction, and electron-phonon interaction. We also discuss the implications and relevant future experiments to observe these phases.