Hierarchy of Floquet gaps and edge states for driven honeycomb lattices

P. M. Perez-Piskunow, L. E. F. Foa Torres, and Gonzalo Usaj
Phys. Rev. A 91, 043625 – Published 20 April 2015

Abstract

Electromagnetic driving in a honeycomb lattice can induce gaps and topological edge states with a structure of increasing complexity as the frequency of the driving lowers. While the high-frequency case is the most simple to analyze we focus on the multiple photon processes allowed in the low-frequency regime to unveil the hierarchy of Floquet edge states. In the case of low intensities an analytical approach allows us to derive effective Hamiltonians and address the topological character of each gap in a constructive manner. At high intensities we obtain the net number of edge states, given by the winding number, with a numerical calculation of the Chern numbers of each Floquet band. Using these methods, we find a hierarchy that resembles that of a Russian nesting doll. This hierarchy classifies the gaps and the associated edge states in different orders according to the electron-photon coupling strength. For large driving intensities, we rely on the numerical calculation of the winding number, illustrated in a map of topological phase transitions. The hierarchy unveiled with the low-energy effective Hamiltonians, along with the map of topological phase transitions, discloses the complexity of the Floquet band structure in the low-frequency regime. The proposed method for obtaining the effective Hamiltonian can be easily adapted to other Dirac Hamiltonians of two-dimensional materials and even the surface of a three-dimensional topological insulator.

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  • Received 4 March 2015

DOI:https://doi.org/10.1103/PhysRevA.91.043625

©2015 American Physical Society

Authors & Affiliations

P. M. Perez-Piskunow1, L. E. F. Foa Torres1, and Gonzalo Usaj2,3

  • 1Instituto de Física Enrique Gaviola (CONICET) and FaMAF, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina
  • 2Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica, 8400 S. C. de Bariloche, Argentina
  • 3Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina

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Issue

Vol. 91, Iss. 4 — April 2015

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