Abstract

In the field of topology, it is commonly accepted that for two-dimensional spin-decoupled structures a complete topological characterization is provided by the Chern numbers of the system[1]. The number of the extraordinarily robust chiral edge modes residing in a band gap is given by the sum of the Chern numbers of all bands below this gap. However, this is strictly true only for systems with a Hamiltonian which is constant in the evolution coordinate. For characterizing periodically driven (Floquet) systems it was shown recently that the appropriate topological invariants are winding numbers [2]. They utilize the information in the Hamiltonian for all times within a single driving period.

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