Analysis of Topological States in a Floquet-driven Non-Hermitian System

Non-Hermitian Hamiltonians offer a good description of many open systems in which gain and loss are present; crucially, in contrast to their Hermtian counterparts, they may have a complex eigenspectrum. Interestingly, non-Hermitian Hamiltonians which possess PT symmetry [1] can be shown to admit an entirely real eigenspectrum within a certain range of their parameters. It has been shown [2] that certain PT-symmetric lattices can admit topologically non-trivial phases; however, this phase only coincides with the PT-symmetry broken phase, and the topological edge states correspond to imaginary eigenvalues. We examine Floquet driving of this system which, for high enough driving frequencies [3], has been shown to stabilize the edge states. By using a simple two-step, pulsed time dependence, we explore the entire range of driving frequencies to highlight new regions of stability, including those which are explicitly below the high-frequency regime.

[1] Bender, C. and Boettcher, S. Phys. Rev. Lett. 80, 5243 (1998)
[2] Rudner, M. S. and Levitov, L. S. Phys. Rev. Lett. 102, 065703 (2009)
[3] C. Yuce, Eur. Phys. J. D 69, 184 (2015)