Topological phases of the kicked Harper–Kitaev model with ultracold atoms

We propose using ultracold atoms trapped in a one-dimensional periodically driven optical lattice to realize the Harper–Kitaev model, where the on-site energies are periodically kicked. Such a system provides a natural platform to study both Chern insulators and Majorana fermions. Based on calculating the quasienergy spectra, we find that both Floquet Majorana modes and Hall chiral edge modes could appear at the sample boundary in the gaps between the quasienergy bands. We also study the competition of topological superconductor and Chern insulator states in the model. We calculate the $Z_2\times Z_2$ index and Floquet Chern number to characterize the above two different topological states, including the topological phase transitions in the kicked Harper–Kitaev model with the increase in the strength of the kick. (paper)