Dynamical Symmetry Breaking in Optically Driven Two-Dimensional Materials

Floquet engineering of bandstructures via application of coherent time-periodic drives is emerging as a powerful tool for creating new types of topological phases of matter. In this talk, I will show how this tool can also be used to induce non-equilibrium correlated states with dynamical spontaneously broken symmetry. I will present two different manifestations of this phenomenon, which are unique to periodically driven systems, and discuss how they can arise in optically driven two dimensional materials. The first involves spontaneously broken quantum liquid crystalline order, with extreme anisotropy whose directionality rotates as a function of time. The second occurs under a slow (and periodical) modulation of the driving amplitude, which drives the system into a steady state with spontenously broken translational symmetry. I will show that the phase transition to these correlated steady states is achieved due to the interplay between the coherent external drive, electron-electron interactions, and dissipative processes arising from the coupling to phonons and the electromagnetic environment. Finaly, I will discuss candidate systems for realizing these non-equilbrium phases of matter, and their interplay with the topology of the underlying Floquet bandstructure.