Universal fluctuations of Floquet topological invariants at low frequencies

M. Rodriguez-Vega, B. Seradjeh

Published 2017-06-16Version 1

We study the low-frequency dynamics of the periodically driven Su-Schrieffer-Heeger model as a prototypical model of a Floquet topological insulator. We show, both analytically and numerically, that in the low frequency limit, $\Omega\rightarrow 0$, the topological invariants of the system exhibit universal fluctuations. While the topological invariants in this limit nearly vanish on average, over a small range of frequencies, we find that they follow a Gaussian distribution with a width that scales as $1/\sqrt{\Omega}$. We explain this scaling based on a diffusive structure of the winding numbers of the Floquet-Bloch evolution operator at low frequency. We also find that the maximum quasienergy gap remains finite and scales as $\Omega^2$. Thus, we argue that the adiabatic limit of a Floquet topological insulator is highly structured, with universal fluctuations persisting down to very low frequencies.