Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice

Mukherjee, Sebabrata; Spracklen, Alexander; Valiente, Manuel; Andersson, Erika; Öhberg, Patrik; Goldman, Nathan; Thomson, Robert R.

doi:10.1038/ncomms13918

Cited by 383 publications

(294 citation statements)

References 45 publications

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“…It will be interesting to study the different impact of symmetries on topological phases, and on the anomalous boundary states that are unique to driven systems, in nature. One way towards realization of the proper symmetries should be offered by photonic crystals 18,19 .…”

Section: Discussionmentioning

confidence: 99%

“…These phases cannot be characterized by static invariants, such as the Chern numbers of the Floquet bands, but only through invariants that depend on the entire dynamical evolution of the system 11 . Irradiated solid state systems [13][14][15] and photonic crystals [16][17][18][19] , where the third spatial dimension represents the time axis, are promising candidates for the realization of these new topological phases.…”

Section: Introductionmentioning

confidence: 99%

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Topological invariants for Floquet-Bloch systems with chiral, time-reversal, or particle-hole symmetry

2018

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We introduce Z2-valued bulk invariants for symmetry-protected topological phases in 2 + 1 dimensional driven quantum systems. These invariants adapt the W3-invariant, expressed as a sum over degeneracy points of the propagator, to the respective symmetry class of the Floquet-Bloch Hamiltonian. The bulk-boundary correspondence that holds for each invariant relates a non-zero value of the bulk invariant to the existence of symmetry-protected topological boundary states. To demonstrate this correspondence we apply our invariants to a chiral Harper, time-reversal KaneMele, and particle-hole symmetric graphene model with periodic driving, where they successfully predict the appearance of boundary states that exist despite the trivial topological character of the Floquet bands. Especially for particle-hole symmetry, combination of the W3 and the Z2-invariants allows us to distinguish between weak and strong topological phases.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Topological invariants for Floquet-Bloch systems with chiral, time-reversal, or particle-hole symmetry

2018

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“…A famous example of this correspondence can be found in the Quantum-Hall effect where the quantization of the Hall conductance is rooted in the current-carrying protected edge states [3][4][5]. The ensemble of (natural and artificial) topological insulators is steadily growing, and these have been by now synthetically engineered in a multitude of physical systems such as atomic [6][7][8][9][10][11], superconducting [12], photonic [13][14][15][16][17] and acoustic platforms [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Topological characterization of chiral models through their long time dynamics

et al. 2018

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We study chiral models in one spatial dimension, both static and periodically driven. We demonstrate that their topological properties may be read out through the long time limit of a bulk observable, the mean chiral displacement. The derivation of this result is done in terms of spectral projectors, allowing for a detailed understanding of the physics. We show that the proposed detection converges rapidly and it can be implemented in a wide class of chiral systems. Furthermore, it can measure arbitrary winding numbers and topological boundaries, it applies to all non-interacting systems, independently of their quantum statistics, and it requires no additional elements, such as external fields, nor filled bands.Topological phases of matter constitute a new paradigm by escaping the standard Ginzburg-Landau theory of phase transitions. These exotic phases appear without any symmetry breaking and are not characterized by a local order parameter, but rather by a global topological order. In the last decade, topological insulators have attracted much interest [1]. These systems are insulators in their bulk but exhibit current carrying edge states protected by the topology. A classification of topological insulators in terms of their discrete symmetries and their spatial dimensionality has been obtained in the celebrated periodic table of topological insulators and superconductors [2]. The topological invariant characterizing these models can be derived from the bulk Hamiltonian and allows one to recover the so called bulk-edge correspondence, namely that the number of topologically protected edge states is proportional to the topological invariant. A famous example of this correspondence can be found in the Quantum-Hall effect where the quantization of the Hall conductance is rooted in the current-carrying protected edge states [3][4][5]. The ensemble of (natural and artificial) topological insulators is steadily growing, and these have been by now synthetically engineered in a multitude of physical systems such as atomic [6][7][8][9][10][11], superconducting [12], photonic [13][14][15][16][17] and acoustic platforms [18][19][20].This work focuses on one-dimensional (1D) topological insulators possessing chiral symmetry. As a consequence of the chiral symmetry, the different sites of the unit cell can always be regarded as part of two sublattices. The topological invariant of the bulk, the winding number  , allows one to predict the number of zero energy edge states. 1D chiral topological insulators have been realized in numerous platforms as ultracold atoms [6,11], photonic crystals [15], photonic quantum walks [21][22][23][24][25]. Let us notice that the 1D chiral Hamiltonian can be static or the effective Hamiltonian of a Floquet system. In the latter case, the topology can be richer than its static counterpart [26][27][28][29]. In both cases, two different approaches to characterize the topology of such systems have been proposed and implemented experimentally. The first one is to look at intrinsic prope...

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“…The authors of this work would like to point out that a related work with similar results is published in ref. 32.…”

Section: Discussionmentioning

confidence: 99%

Observation of photonic anomalous Floquet topological insulators

Maczewsky¹,

Zeuner²,

Nolte³

et al. 2017

Nat Commun

479

325

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Topological insulators are a new class of materials that exhibit robust and scatter-free transport along their edges — independently of the fine details of the system and of the edge — due to topological protection. To classify the topological character of two-dimensional systems without additional symmetries, one commonly uses Chern numbers, as their sum computed from all bands below a specific bandgap is equal to the net number of chiral edge modes traversing this gap. However, this is strictly valid only in settings with static Hamiltonians. The Chern numbers do not give a full characterization of the topological properties of periodically driven systems. In our work, we implement a system where chiral edge modes exist although the Chern numbers of all bands are zero. We employ periodically driven photonic waveguide lattices and demonstrate topologically protected scatter-free edge transport in such anomalous Floquet topological insulators.

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Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice

Cited by 383 publications

References 45 publications

Topological invariants for Floquet-Bloch systems with chiral, time-reversal, or particle-hole symmetry

Topological invariants for Floquet-Bloch systems with chiral, time-reversal, or particle-hole symmetry

Topological characterization of chiral models through their long time dynamics

Observation of photonic anomalous Floquet topological insulators

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