Floquet topological phases of higher winding numbers in extended Su-Schrieffer-Heeger model under quenched drive

Abstract: In this study topological properties of static and dynamic Su-Schrieffer-Heeger models with staggered further neighbor hopping terms of different extents are investigated. Topological characterization of the static chiral models is established in terms of conventional winding number while Floquet topological character is studied by a pair of winding numbers. With the increase of extent of further neighbor terms topological phases with higher winding numbers are found to emerge in both static and dynamic systems. Topological phase diagrams of static models for four different extents of further neighbor terms are presented, which has been generalized for arbitrary extent afterwards. Similarly, Floquet topological phase diagrams of four such dynamic models have been presented. For every model four different parametrizations of hopping terms are introduced which exhibits different patterns of topological phase diagrams. In each case emergence of 0' and$\pi$' energy edge states is noted and they are found to consistent to the bulk-boundary correspondence rule applicable for chiral topological systems.