Noise resilience of two-dimensional Floquet topological phases

We study the effect of noise on two-dimensional periodically driven topological phases, focusing on two examples: the anomalous Floquet-Anderson phase and the disordered Floquet-Chern phase. Both phases show an unexpected robustness against timing noise. The noise-induced decay of initially populated topological edge modes occurs in two stages: At short times, thermalization among edge modes leads to exponential decay. This is followed by slow algebraic decay <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mo>∼</a:mo> <a:msup> <a:mi>n</a:mi> <a:mrow> <a:mo>−</a:mo> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> </a:msup> </a:mrow> </a:math> with the number of Floquet cycles <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>n</b:mi> </b:math> . The exponent of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mn>1</c:mn> <c:mo>/</c:mo> <c:mn>2</c:mn> </c:mrow> </c:math> is characteristic for one-dimensional diffusion, here occurring along the direction perpendicular to the edge. In contrast, localized modes in the bulk exhibit faster decay, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mo>∼</d:mo> <d:msup> <d:mi>n</d:mi> <d:mrow> <d:mo>−</d:mo> <d:mn>1</d:mn> </d:mrow> </d:msup> </d:mrow> </d:math> , corresponding to two-dimensional diffusion. We demonstrate these behaviors through full-scale numerical simulations and support our conclusions using analytical results based upon a phenomenological model. Our findings indicate that two-dimensional Floquet topological phases are ideal candidates for potential applications of Floquet topology, given the unavoidable presence of both quenched disorder and decoherence in experiments.