Bulk-edge correspondence for Floquet topological phases in honeycomb nanoribbon

Abstract

Possibility of having different topological phases by time-periodic external field encourages people who wish to manipulate the properties of the materials as their will for the various kinds of systems including a honeycomb nanoribbon. We study bulk-edge correspondence by looking at the change in the value of the first Chern number of a specific band, which reflects the bulk properties, together with the change of associated edge states in quasienergy spectrum when the honeycomb nanoribbon is exposed to circularly polarized laser field. Various topological phase transitions are observed as the intensity of the laser field is raised up and we classify them in two categories. In the first category, when the frequency is sufficiently high, the system undergoes simple transition from trivial phase to topological one, reflected by the sudden jump in the value of Chern number from 0 to 1 and the appearance of two crossing edge states in the spectrum. Whereas, in the second category where the frequency is low enough, anomalous transitions are drawn, having several nonzero values of Chern number, and band folding prevails, often disappearing depending on the laser intensities. The results confirm the bulk-edge correspondence in periodically driven systems and will contribute to future material designs.