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Register a new userTopological origin of quantized transport in non-Hermitian Floquet chains
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We show that non-Hermiticity enables topological phases with unidirectional transport in one-dimensional Floquet chains. The topological signatures of these phases are non-contractible loops in the spectrum of the Floquet propagator that are separated by an imaginary gap. Such loops occur exclusively in non-Hermitian Floquet systems. We define the corresponding topological invariant as the winding number of the Floquet propagator relative to the imaginary gap. To relate topology to transport, we introduce the concept of regularized dynamics of non-Hermitian chains. We establish that, under the conditions of regularized dynamics, transport is quantized in so far as the charge transferred over one period equals the topological winding number. We illustrate these theoretical findings with the example of a Floquet chain that features a topological phase transition and acts as a charge pump in the non-trivial topological phase. We finally discuss whether these findings justify the notion that non-Hermitian Floquet chains support topological transport.
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We show how quantized transport can be realized in Floquet chains through encapsulation of a chiral or helical shift. The resulting transport is immutable rather than topological in the sense that it neither requires a band gap nor is affected by arbitrarily strong perturbations. Transport is still characterized by topological quantities but encapsulation of the shift prevents topological phase transitions. To explore immutable transport we introduce the concept of a shiftbox, explain the relevant topological quantities both for momentum-space dispersions and real-space transport, and study model systems of Floquet chains with strictly quantized chiral and helical transport. Natural platforms for the experimental investigation of these scenarios are photonic Floquet chains constructed in waveguide arrays, as well as topolectrical or mechanical systems.
In Hermitian topological systems, the bulk-boundary correspondence strictly constraints boundary transport to values determined by the topological properties of the bulk. We demonstrate that this constraint can be lifted in non-Hermitian Floquet insulators. Provided that the insulator supports an anomalous topological phase, non-Hermiticity allows us to modify the boundary states independently of the bulk, without sacrificing their topological nature. We explore the ensuing possibilities for a Floquet topological insulator with non-Hermitian time-reversal symmetry, where the helical transport via counterpropagating boundary states can be tailored in ways that overcome the constraints imposed by Hermiticity. Non-Hermitian boundary state engineering specifically enables the enhancement of boundary transport relative to bulk motion, helical transport with a preferred direction, and chiral transport in the same direction on opposite boundaries. We explain the experimental relevance of our findings for the example of photonic waveguide lattices.
Topological phenomena in non-Hermitian systems have recently become a subject of great interest in the photonics and condensed-matter communities. In particular, the possibility of observing topologically-protected edge states in non-Hermitian lattices has sparked an intensive search for systems where this kind of states are sustained. Here, we present the first study on the emergence of topological edge states in two-dimensional Haldane lattices exhibiting balanced gain and loss. In line with recent studies on other Chern insulator models, we show that edge states can be observed in the so-called broken $mathcal{P}mathcal{T}$-symmetric phase, that is, when the spectrum of the gain-loss-balanced systems Hamiltonian is not entirely real. More importantly, we find that such topologically protected edge states emerge irrespective of the lattice boundaries, namely zigzag, bearded or armchair.
We demonstrate that dislocations in two-dimensional non-Hermitian systems can give rise to density accumulation or depletion through the localization of an extensive number of states. These effects are shown by numerical simulations in a prototype lattice model and expose a completely new face of non-Hermitian skin effect, by disentangling it from the need for boundaries. We identify a topological invariant responsible for the dislocation skin effect, which takes the form of a ${mathbb Z}_2$ Hopf index that depends on the Burgers vector characterizing the dislocations. Remarkably, we find that this effect and its corresponding signature for defects in Hermitian systems falls outside of the known topological classification based on bulk-defect correspondence.
The topological phases of periodically-driven, or Floquet systems, rely on a perfectly periodic modulation of system parameters in time. Even the smallest deviation from periodicity leads to decoherence, causing the boundary (end) states to leak into the systems bulk. Here, we show that in one dimension this decay of topologically protected end states depends fundamentally on the nature of the bulk states: a dispersive bulk results in an exponential decay, while a localized bulk slows the decay down to a diffusive process. The localization can be due to disorder, which remarkably counteracts decoherence even when it breaks the symmetry responsible for the topological protection. We derive this result analytically, using a novel, discrete-time Floquet-Lindblad formalism and confirm out findings with the help of numerical simulations. Our results are particularly relevant for experiments, where disorder can be tailored to protect Floquet topological phases from decoherence.
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