Floquet edge state protection in non-Hermitian topological systems

Andrew Harter (U. Tokyo)

In previous works [1], we have considered a two-level system with time periodic (Floquet), PT-symmetric [2] gain and loss. Although this system is generically non-Hermitian, at any instant, the system may be in a broken or unbroken PT-symmetric phase, and its long-term behavior is governed by an effective Floquet Hamiltonian. Interestingly, the PT phase diagram for this system features a re-entrant PT unbroken phase, in which, as the driving frequency is swept from zero (static) to near the natural resonance frequency, the system enters the PT-broken phase; however, if the driving frequency is sufficiently increased, the system will re-enter the PT-unbroken phase again. 
Recently, we have applied this type of PT-symmetric, Floquet driving to the one-dimensional Su-Schrieffer-Heeger (SSH) model, which exhibits a topologically nontrivial phase. In the static case [3], the edge states are pushed into far ends of the energy spectrum in the imaginary plane [4]. In contrast, for the time-periodic case, the Floquet energy spectrum provides a periodically repeating structure in the frequency domain, and we have analyzed the possible stabilizing effect this can have on the topologically relevant states.

[1] Li, J., Harter, A., Liu, J., de Melo, L., Joglekar, Y. and Luo, L. Nat. Comms. 10, 855, (2019)
[2] Bender, C. and Boettcher, S. Phys. Rev. Lett. 80, 5243 (1998) 
[3] Rudner, M. S. and Levitov, L. S. Phys. Rev. Lett.102, 065703 (2009)
[4] Hu, Y. C. and Hughes, T. L. Phys. Rev. B 84, 153101 (2011)