Dual topological characterization of non-Hermitian Floquet phases

Abstract

Non-Hermiticity is expected to add far more physical features to the already rich Floquet topological phases of matter. Nevertheless, a systematic approach to characterize non-Hermitian Floquet topological matter is still lacking. In this work we introduce a dual scheme to characterize the topology of non-Hermitian Floquet systems in momentum space and in real space, using a piecewise quenched nonreciprocal Su-Schrieffer-Heeger model for our case studies. Under the periodic boundary condition, topological phases are characterized by a pair of experimentally accessible winding numbers that make jumps between integers and half-integers. Under the open boundary condition, a Floquet version of the so-called open boundary winding number is found to be integers and can predict the number of pairs of zero and $\pi$ Floquet edge modes coexisting with the non-Hermitian skin effect. Our results indicate that a dual characterization of non-Hermitian Floquet topological matter is necessary and also feasible because the formidable task of constructing the celebrated generalized Brillouin zone for non-Hermitian Floquet systems with multiple hopping length scales can be avoided. This work hence paves a way for further studies of non-Hermitian physics in non-equilibrium systems.

11 pages, 9 figures, comments are welcome

References in corpus (9)

• Topological Origin of Non-Hermitian Skin Effects
• Topological Transition in a Non-Hermitian Quantum Walk
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
• Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
• Dynamical signatures of topological order in the driven-dissipative Kitaev chain
• A computational study of two-terminal transport of Floquet quantum Hall insulators
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder

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• Non-Hermitian topological phases and dynamical quantum phase transitions: A generic connection
• Symmetry and topological classification of Floquet non-Hermitian systems
• Driving-induced multiple $\mathcal{P}\mathcal{T}$-symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals
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• Entanglement transitions in a periodically driven non-Hermitian Ising chain
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• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
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• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
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