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The high Chern number phases with the Chern number |C| > 1 are observed inthis study of a periodically driven extended Su-Schrieffer-Heeger (E-SSH) modelwith a cyclic parameter. Besides the standard intra-dimer and thenearest-neighbor (NN) inter-dimer hopping of the SSH model, an additionalnext-nearest-neighbor (NNN) hopping is considered in the E-SSH model. Thecyclic parameter, which plays the role of a synthetic dimension, is invoked asa modulation of the hopping strengths. A rigorous analysis of different phasediagrams has shown multiple Floquet topological phase transitions among thehigh Chern number phases. These phase transitions can be controlled by thestrength and frequency of the periodic driving. Instead of applyingperturbation theory, the whole analysis is done by Floquet replica technique.This gives a freedom to study high as well as low-frequency effects on thesystem by considering less or more number of photon sectors. This system can beexperimentally realized through a pulse sequence scheme in the optical latticesetup.

Floquet topological phases with high Chern numbers in a periodically driven extended Su-Schrieffer-Heeger model