Cutting off the non-Hermitian boundary from an anomalous Floquet topological insulator
TL;DR: In this article, the authors show that the topological properties of such spectrally separated boundary states are no longer restricted by the strict bulk-boundary correspondence of Hermitian systems and show that this additional topological freedom enables one to faithfully transfer the topology properties of a boundary attached to a Floquet insulator to a non-Hermitian Floquet chain obtained by physically cutting off the boundary from the bulk.
Abstract: In two-dimensional anomalous Floquet insulators, non-Hermitian boundary state engineering can be used to completely separate chiral boundary states from bulk bands in the quasienergy spectrum. The topological properties of such spectrally separated boundary states are no longer restricted by the strict bulk-boundary correspondence of Hermitian systems. We show that this additional topological freedom enables one to faithfully transfer the topological properties of a boundary attached to a Floquet insulator to a non-Hermitian Floquet chain obtained by physically cutting off the boundary from the bulk. We implement this scenario for a simple model of an anomalous Floquet insulator with Hermitian and non-Hermitian boundaries, and discuss the relevance of our construction for the experimental realization of non-Hermitian topological phases that connect dimensions one and two.
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TL;DR: In this paper, a light-driven platform for controlling exceptional points in non-Hermitian topological systems has been proposed and demonstrated using three different topological models: nodal line semimetals, semi-Dirac semi-metals, and Dirac semimimetals.
Abstract: We propose and show that application of light leads to an intriguing platform for controlling exceptional points in non-Hermitian topological systems. We demonstrate our proposal using three different non-Hermitian systems---nodal line semimetals, semi-Dirac semimetals, and Dirac semimetals---and show that using illumination with light one can engineer the positions and stability of exceptional points. We illustrate the topological properties of these models and map out their light-driven topological phase transitions.
13 citations
TL;DR: In this article , anomalous Floquet topological insulators generate intrinsic, non-Hermitian topology on their boundary, which is a consequence of the nontrivial topology of the bulk Floquet operator.
Abstract: We show that anomalous Floquet topological insulators generate intrinsic, non-Hermitian topology on their boundary. As a consequence, removing a boundary hopping from the time-evolution operator stops the propagation of chiral edge modes, leading to a non-Hermitian skin effect. This does not occur in Floquet Chern insulators, however, in which boundary modes continue propagating. The non-Hermitian skin effect on the boundary is a consequence of the nontrivial topology of the bulk Floquet operator, which we show by designing a real-space topological invariant. Our work introduces a form of `mixed' higher-order topology, providing a bridge between research on periodically-driven systems and the study of non-Hermiticity. It suggests that periodic driving, which has already been demonstrated in a wide range of experiments, may be used to generate non-Hermitian skin effects.
3 citations
12 Jan 2021
TL;DR: In this paper, the authors proposed a one-dimensional Floquet ladder that possesses two distinct topological transport channels with opposite directionality and showed that the direction of transport in the resulting waveguide structure can be externally controlled by focusing two light beams into adjacent waveguides.
Abstract: We propose a one-dimensional Floquet ladder that possesses two distinct topological transport channels with opposite directionality. The transport channels occur due to a Z2 non-Hermitian Floquet topological phase that is protected by time-reversal symmetry. The signatures of this phase are two pairs of Kramers degenerate Floquet quasienergy bands that are separated by an imaginary gap. We discuss how the Floquet ladder can be implemented in a photonic waveguide lattice and show that the direction of transport in the resulting waveguide structure can be externally controlled by focusing two light beams into adjacent waveguides. The relative phase between the two light beams selects which of the two transport channels is predominantly populated, while the angles of incidence of the two light beams determine which of the transport channels is suppressed by non-Hermitian losses. We identify the optimal lattice parameters for the external control of transport and demonstrate the robustness of this mechanism against disorder.
2 citations
TL;DR: In this paper, a non-Hermitian Floquet model with topological edge states in real and imaginary band gaps is presented, which utilizes two stacked honeycomb lattices which can be related via four different types of non-hermitian time reversal symmetry.
Abstract: We present a non-Hermitian Floquet model with topological edge states in real and imaginary band gaps. The model utilizes two stacked honeycomb lattices which can be related via four different types of non-Hermitian time-reversal symmetry. Implementing the correct time-reversal symmetry provides us with either two counterpropagating edge states in a real gap, or a single edge state in an imaginary gap. The counterpropagating edge states allow for either helical or chiral transport along the lattice perimeter. In stark contrast, we find that the edge state in the imaginary gap does not propagate. Instead, it remains spatially localized while its amplitude continuously increases. Our model is well-suited for realizing these edge states in photonic waveguide lattices.
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TL;DR: In this article, the authors introduce non-Hermitian Floquet engineering as a new concept to overcome the problem of quantized particle transport in slowly varying potentials (Thouless pumping) and predict that a topological band structure and associated quantized transport can be restored at driving frequencies as large as the system's band gap.
Abstract: Quantized dynamics is essential for natural processes and technological applications alike. The work of Thouless on quantized particle transport in slowly varying potentials (Thouless pumping) has played a key role in understanding that such quantization may be caused not only by discrete eigenvalues of a quantum system, but also by invariants associated with the nontrivial topology of the Hamiltonian parameter space. Since its discovery, quantized Thouless pumping has been believed to be restricted to the limit of slow driving, a fundamental obstacle for experimental applications. Here, we introduce non-Hermitian Floquet engineering as a new concept to overcome this problem. We predict that a topological band structure and associated quantized transport can be restored at driving frequencies as large as the system's band gap. The underlying mechanism is suppression of non-adiabatic transitions by tailored, time-periodic dissipation. We confirm the theoretical predictions by experiments on topological transport quantization in plasmonic waveguide arrays.
39 citations
TL;DR: In this paper, a two-dimensional, discrete-time quantum walk exhibiting non-Hermitian skin effects under open-boundary conditions was constructed, and the emergence of topological edge states were consistent with Floquet winding numbers calculated using a non-Bloch band theory invoking time-dependent generalized Billouin zones.
Abstract: We construct a two-dimensional, discrete-time quantum walk exhibiting non-Hermitian skin effects under open-boundary conditions. As a confirmation of the non-Hermitian bulk-boundary correspondence, we show that the emergence of topological edge states are consistent with Floquet winding numbers calculated using a non-Bloch band theory invoking time-dependent generalized Billouin zones. Further, the non-Bloch topological invariants associated with quasienergy bands are captured by a non-Hermitian local Chern marker in real space, defined through local biorthogonal eigen wave functions of the non-unitary Floquet operator. Our work would stimulate further studies of non-Hermitian Floquet topological phases where skin effects play a key role.
6 citations