Adding Doublons to a Floquet-Topological Insulator

We characterize a Floquet-topological insulator on a finite square lattice with a linear defect in the form of an additional on-site potential along the diagonal.

In addition to the usual bulk and edge states, this system also exhibits doublon states on its primary and secondary diagonals. The doublons' energies increase with the diagonal potential, which leads to a rich band structure, including crossings and avoided crossings with other states.

In real-time propagation, an edge state traveling along the boundary of the system will split when hitting the linear defect and continue propagating along the edge and the diagonal simultaneously. The strength of the diagonal potential determines the ratio between both parts. This behavior could allow for the non-destructive measurement of topological edge states. Investigating shorter defects, which affect only some sites on the diagonal, we find and explain a temporal delay between the two contributions traveling around and through the defect.