Robustness of Floquet Topology to Temporal Noise

Previous studies on two dimensional periodically driven Floquet systems have demonstrated a novel topological phase known as the anomalous Floquet insulator (AFI). The AFI has quantized, non-adiabatic charge pumping, carried by the chiral edge states of the system. Unlike a Chern insulator, the AFI is able to be localized in the bulk, and this topological response is robust to adding spatial disorder. We consider a more disruptive perturbation, adding temporal noise to each of the Floquet cycles to break the time periodicity. We solve this system numerically in a cylindrical geometry starting from a half-filled state and calculating the net charge pumped around the cylinder during each Floquet period. Surprisingly, we see that the quantization remains for a finite window of temporal disorder up to a time that increases as a power law in system size. We connect the eventual loss of quantization to diffusion of the charge front, which eventually depopulates the topological edge state. This work provides an important insight to how topological Floquet phases might behave in real materials, where noise from the bath is inevitable.