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The topological phases of periodically-driven, or Floquet systems, rely on aperfectly periodic modulation of system parameters in time. Even the smallestdeviation from periodicity leads to decoherence, causing the boundary (end)states to leak into the system's bulk. Here, we show that in one dimension thisdecay of topologically protected end states depends fundamentally on the natureof the bulk states: a dispersive bulk results in an exponential decay, while alocalized bulk slows the decay down to a diffusive process. The localizationcan be due to disorder, which remarkably counteracts decoherence even when itbreaks the symmetry responsible for the topological protection. We derive thisresult analytically, using a novel, discrete-time Floquet-Lindblad formalismand confirm out findings with the help of numerical simulations. Our resultsare particularly relevant for experiments, where disorder can be tailored toprotect Floquet topological phases from decoherence.

Localization counteracts decoherence in noisy Floquet topological chains