Dual topological characterization of non-Hermitian Floquet phases
TL;DR: In this article, a dual scheme to characterize the topology of non-Hermitian Floquet systems in momentum space and in real space using a piecewise quenched non-reciprocal Su-Schrieffer-Heeger model is introduced.
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 $\ensuremath{\pi}$ 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 nonequilibrium systems.
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15 Jun 2021
TL;DR: In this paper, non-hermiticity by loss can induce topological phase transition of a Floquet system, and non-Hermiticity-by-loss is shown to induce a topological transition of Floquet systems.
Abstract: This paper shows that non-Hermiticity by loss can induce topological phase transition of a Floquet system .
20 citations
TL;DR: In this paper, the authors report the light-driven exceptional physics in a multi-Weyl semimetal and demonstrate topological charge distribution and Lifshitz transition, which are controllable by the driving field in such generated ECs.
Abstract: Non-Hermitian topological systems are the newest additions to the growing field of topological matter. In this work, we report the light-driven exceptional physics in a multi-Weyl semimetal. The driving is not only a key ingredient to control the position of the exceptional contours (ECs); light also has the ability to generate new ECs. Interestingly, we also demonstrate topological charge distribution and Lifshitz transition, which are controllable by the driving field in such generated ECs. Our findings present a promising platform for the manipulation and control over exceptional physics in non-Hermitian topological matter.
19 citations
DOI•
TL;DR: In this article , the authors proposed a generic approach to hybrid skin-topological modes with gain and loss, where the anomalous Floquet band topology is no longer captured by band Chern numbers.
Abstract: : Non-Hermitian skin effect (NHSE) in non-Hermitian lattice systems, associated with a point gap on the complex energy plane, has attracted great theoretical and experimental interest. Much less is studied on the so-called second-order non-Hermitian skin effect, where the bulk does not support a point gap but localization at the corner still occurs. This work discovers a class of hybrid skin-topological modes as the second-order non-Hermitian skin effect without asymmetric couplings. Specifically, by only adding gain/loss to two-dimensional Chern insulators and so long as the gain/loss strength does not close the line gap, all the topological edge states are localized at one corner under the open boundary condition, with the bulk states extended. The resultant non-Hermitian Chern bands can be still topologically characterized by Chern numbers, whereas the hybrid skin-topological modes are understood via some auxiliary Hermitian systems that belong to either intrinsic or extrinsic second-order topological insulator phases. By proposing an innovative construction of auxiliary Hamiltonian, our generic route to hybrid skin-topological modes is further successfully extended to nonequilibrium topological systems with gain and loss, where the anomalous Floquet band topology is no longer captured by band Chern numbers. The extension thus leads to the intriguing finding of nonequilibrium hybrid skin-topological modes. In addition to offering a straightforward route to experimental realization of hybrid topological-skin effects, this study also opens up a promising perspective for the understanding of corner localization by revealing the synergy of three important concepts, namely, non-Hermitian topological insulator, second-order non-Hermitian skin effect, and second-order topological insulator.
15 citations
23 Aug 2021
TL;DR: In this article, the authors find dynamically controlled localization transitions and mobility edges in non-Hermitian quasicrystals via shaking the lattice periodically, which can endow a system with peculiar topological and transport features.
Abstract: Time-periodic driving fields could endow a system with peculiar topological and transport features. In this work, we find dynamically controlled localization transitions and mobility edges in non-Hermitian quasicrystals via shaking the lattice periodically. The driving force dresses the hopping amplitudes between lattice sites, yielding alternate transitions between localized, mobility edge, and extended non-Hermitian quasicrystalline phases. We apply our Floquet engineering approach to five representative models of non-Hermitian quasicrystals, obtain the conditions of photon-assisted localization transitions and mobility edges, and find the expressions of Lyapunov exponents for some models. We further introduce topological winding numbers of Floquet quasienergies to distinguish non-Hermitian quasicrystalline phases with different localization nature. Our discovery thus extend the study of quasicrystals to non-Hermitian Floquet systems, and provide an efficient way of modulating the topological and transport properties of these unique phases.
15 citations
TL;DR: In this paper , the authors show that non-Hermitian loss/gain can generate an exceptional hexagonal warping effect in double Weyl semimetals (DWSMs), which has distinctive effects on Fermi surface topology.
Abstract: Hexagonal warping (HW) in three-dimensional topological insulators is, by now, well known. We show that non-Hermitian (NH) loss/gain can generate an exceptional HW effect in double Weyl semimetals (DWSMs). This unique feature of DWSMs has distinctive effects on Fermi surface topology. Importantly, in the presence of such a ${k}^{3}$ spin orbit coupling mimicking term, the symmetry associated with the DWSMs is changed, leading to four exceptional points, among which two are degenerate. Introducing a driving field removes this degeneracy. The combined action of the NH warping and driving parameters leads to notable effects, including merging and tuning of exceptional points. We analyze the topological nature of the generated exceptional contours by evaluating several topological invariants, such as winding number, vorticity, and NH Berry curvature. We hope that our theoretical results will initiate possible experiments exploring NH HW effects.
14 citations
References
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TL;DR: In this article, a spin-1/2 system on a honeycomb lattice is studied, where the interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength.
4,032 citations
"Dual topological characterization o..." refers background in this paper
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...In terms of Q, an openboundary winding number (OBWN) can be introduced as ν = 1 LB TrB(SQ[Q,N ]) [40, 56–58]....
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TL;DR: This work proposes and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport—a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges.
Abstract: Topological insulators are a new phase of matter, with the striking property that conduction of electrons occurs only on their surfaces. In two dimensions, electrons on the surface of a topological insulator are not scattered despite defects and disorder, providing robustness akin to that of superconductors. Topological insulators are predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Substantial effort has been directed towards realizing topological insulators for electromagnetic waves. One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional and therefore exhibit no transport properties. Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect, by placing a gyromagnetic photonic crystal in an external magnetic field. But because magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatter-free edge states requires a fundamentally different mechanism-one that is free of magnetic fields. A number of proposals for photonic topological transport have been put forward recently. One suggested temporal modulation of a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states. This is in the spirit of the proposed Floquet topological insulators, in which temporal variations in solid-state systems induce topological edge states. Here we propose and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport-a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides arranged in a graphene-like honeycomb lattice. Paraxial diffraction of light is described by a Schrodinger equation where the propagation coordinate (z) acts as 'time'. Thus the helicity of the waveguides breaks z-reversal symmetry as proposed for Floquet topological insulators. This structure results in one-way edge states that are topologically protected from scattering.
2,483 citations
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...–Floquet topological phases, as created by time-periodic modulations, have been an experimental reality in both synthetic metamaterials [1–4] and actual condensed-matter systems [5, 6]....
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TL;DR: This work obtains the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by theNon-Bloch winding number instead of the Bloch-Hamiltonian-based topological number.
Abstract: The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates redefinition of topological invariants in a generalized Brillouin zone. The resultant phase diagrams dramatically differ from the usual Bloch theory. Specifically, we obtain the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by the non-Bloch winding number instead of the Bloch-Hamiltonian-based topological number. Our work settles the issue of the breakdown of conventional bulk-boundary correspondence and introduces the non-Bloch bulk-boundary correspondence.
1,326 citations
"Dual topological characterization o..." refers background in this paper
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...Second, the so-called non-Hermitian skin effect (NHSE) [38–45], which corresponds to the pile up of bulk states at the edges of a non-Hermitian lattice, must also be well addressed for a topological characterization aiming at predicting the emergence of many topological edge modes, localized not because of NHSE, but topological localization....
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TL;DR: Using time- and angle-resolved photoemission spectroscopy, it is shown that an intense ultrashort midinfrared pulse with energy below the bulk band gap hybridizes with the surface Dirac fermions of a topological insulator to form Floquet-Bloch bands.
Abstract: The unique electronic properties of the surface electrons in a topological insulator are protected by time-reversal symmetry. Circularly polarized light naturally breaks time-reversal symmetry, which may lead to an exotic surface quantum Hall state. Using time- and angle-resolved photoemission spectroscopy, we show that an intense ultrashort midinfrared pulse with energy below the bulk band gap hybridizes with the surface Dirac fermions of a topological insulator to form Floquet-Bloch bands. These photon-dressed surface bands exhibit polarization-dependent band gaps at avoided crossings. Circularly polarized photons induce an additional gap at the Dirac point, which is a signature of broken time-reversal symmetry on the surface. These observations establish the Floquet-Bloch bands in solids and pave the way for optical manipulation of topological quantum states of matter.
859 citations
"Dual topological characterization o..." refers background in this paper
...–Floquet topological phases, as created by time-periodic modulations, have been an experimental reality in both synthetic metamaterials [1–4] and actual condensed-matter systems [5, 6]....
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...1038/s41567-020-0949-y [5] Y....
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TL;DR: In this paper, the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed.
Abstract: The current understanding of the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed. In particular, how the paramount and genuinely NH concept of exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, leads to phenomena drastically distinct from the familiar Hermitian realm is discussed. An immediate consequence is the ubiquitous occurrence of nodal NH topological phases with concomitant open Fermi-Seifert surfaces, where conventional band-touching points are replaced by the aforementioned exceptional degeneracies. Furthermore, new notions of gapped phases including topological phases in single-band systems are detailed, and the manner in which a given physical context may affect the symmetry-based topological classification is clarified. A unique property of NH systems with relevance beyond the field of topological phases consists of the anomalous relation between bulk and boundary physics, stemming from the striking sensitivity of NH matrices to boundary conditions. Unifying several complementary insights recently reported in this context, a picture of intriguing phenomena such as the NH bulk-boundary correspondence and the NH skin effect is put together. Finally, applications of NH topology in both classical systems including optical setups with gain and loss, electric circuits, and mechanical systems and genuine quantum systems such as electronic transport settings at material junctions and dissipative cold-atom setups are reviewed.
758 citations