Floquet topological phase transitions and the anomalous Floquet Anderson insulator in a continuously driven optical lattice with disorder

The impact of disorder and its spatial correlation on the topology of a Floquet system is not well understood so far. For example, the anomalous Floquet Anderson insulator (AFAI) has been theoretically predicted in step-wise periodically driven models, but its stability under more general driving protocols has not been determined. In this study we investigate a model closely related to a two-dimensional Floquet system that has been realized with a continuous driving protocol in the experiment by K. Wintersperger et. al., Nat. Phys. 16, 1058 (2020). In the absence of disorder, we determine the phase diagram and identify a new phase characterized by edge states with alternating chirality in adjacent gaps. In the presence of weak disorder, we examine the disorder-averaged Bott index and analyze why the anomalous Floquet topological insulator is favored by both uncorrelated and correlated disorder, with the latter having a stronger effect. We furthermore show that adding disorder to the anomalous Floquet topological insulator in this system can lead to an AFAI phase, where, for a range of disorder strengths, all time-averaged bulk states become localized, while the pumped charge in a Laughlin pump setup remains quantized.