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We study the low-frequency dynamics of periodically driven one-dimensional systems hosting Floquet topological phases. We show, both analytically and numerically, in the low-frequency limit $Omegato0$, the topological invariants of a chirally-symmetric driven 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 universal 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.
We introduce $mathbb Z_2$-valued bulk invariants for symmetry-protected topological phases in $2+1$ dimensional driven quantum systems. These invariants adapt the $W_3$-invariant, expressed as a sum over degeneracy points of the propagator, to the re
We develop a theory of topological transitions in a Floquet topological insulator, using graphene irradiated by circularly polarized light as a concrete realization. We demonstrate that a hallmark signature of such transitions in a static system, i.e
A key feature of topological insulators (TI) is symplectic symmetry of the Hamiltonian which changes to unitary when time reversal symmetry is lifted and the topological phase transition occurs. However, such a crossover has never been explicitly obs
We report on van der Waals epitaxial growth, materials characterization and magnetotransport experiments in crystalline nanosheets of Bismuth Telluro-Sulfide (BTS). Highly layered, good-quality crystalline nanosheets of BTS are obtained on SiO$_2$ an
Periodically driven systems can host so called anomalous topological phases, in which protected boundary states coexist with topologically trivial Floquet bulk bands. We introduce an anomalous version of reflection symmetry protected topological crys