Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect

Abstract

Periodically driven non-Hermitian systems can exhibit rich topological band structure and non-Hermitian skin effect, without analogs in their static or Hermitian counterparts. In this work we investigate the exceptional band-touching points in the Floquet quasi-energy bands, the topological characterization of such exceptions points and the Floquet non-Hermitian skin effect (FNHSE). Specifically, we exploit the simplicity of periodically quenched two-band systems in one dimension or two dimensions to analytically obtain the Floquet effective Hamiltonian as well as locations of the many exceptional points possessed by the Floquet bulk bands. Two different types of topological winding numbers are used to characterize the topological features. Bulk-edge correspondence (BBC) is naturally found to break down due to FNHSE, which can be drastically different among different bulk states. Remarkably, given the simple nature of our model systems, recovering the BBC is doable in practice only for certain parameter regime where a low-order truncation of the characteristic polynomial (which determines the Floquet band structure) becomes feasible. Furthermore, irrespective of which parameter regime we work with, we find a number of intriguing aspects of Floquet topological zero modes and $\pi$ modes. For example, under the open boundary condition zero edge modes and $\pi$ edge modes can individually coalesce and localize at two different boundaries. These anomalous edge states can also switch their accumulation boundaries when certain system parameter is tuned. These results indicate that non-Hermitian Floquet topological phases, though more challenging to understand than their Hermitian counterparts, can be extremely rich in the presence of FNHSE.

14 pages, 10 figures

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• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder
• Realizing exceptional points by Floquet dissipative couplings in thermal atoms
• Two-dimensional anisotropic non-Hermitian Lieb lattice
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Controlling the direction of topological transport in a non-Hermitian time-reversal symmetric Floquet ladder
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Floquet multiple exceptional points with higher-order skin effect
• Self-healing of non-Hermitian topological skin modes
• Floquet spin textures in optically pumped non-Hermitian surface states
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems
• Liouvillian topology and nonreciprocal dynamics in open Floquet chains