Anomalous bulk-edge correspondence in continuous media

@article{Tauber2019AnomalousBC,
  title={Anomalous bulk-edge correspondence in continuous media},
  author={C. Tauber and Pierre Delplace and A. Venaille},
  journal={arXiv: Mesoscale and Nanoscale Physics},
  year={2019}
}
Topology plays an increasing role in physics beyond the realm of topological insulators in condensed mater. From geophysical fluids to active matter, acoustics or photonics, a growing family of systems presents topologically protected chiral edge modes. The number of such modes should coincide with the bulk topological invariant (e.g. Chern number) defined for a sample without boundary, in agreement with the bulk-edge correspondence. However this is not always the case when dealing with… Expand

Figures and Tables from this paper

Physical Violations of the Bulk-Edge Correspondence in Topological Electromagnetics.
TLDR
The correspondence principle is physically violated for all practical purposes, as a result of the unavoidable attenuation of highly confined modes even if all materials are assumed perfect, with zero intrinsic bulk losses, due to confinement-induced Landau damping or nonlocality-induced radiation leakage. Expand
Chern Invariants of Topological Continua; a Self-Consistent Nonlocal Hydrodynamic Model
The bulk-edge correspondence is a fundamental principle of topological wave physics, which states that the difference in gap Chern numbers between the interfaced materials is equal to the net numberExpand
Topology in shallow-water waves: A spectral flow perspective
In the context of topological insulators, the shallow-water model was recently shown to exhibit an anomalous bulk-edge correspondence, rooted in the unbounded nature of the spectrum. For the modelExpand
Topological invariants for interface modes
  • G. Bal
  • Physics, Mathematics
  • 2019
We consider topologically non-trivial interface Hamiltonians, which find applications in materials science and geophysical fluid flows. The non-trivial topology manifests itself in the existence ofExpand
Topological active matter
In this review, we summarize recent progress in understanding the role and relevance of topological excitations in a special category of systems called active matter. Active matter is a class ofExpand
Wavefront dislocations reveal insulator topology
Phase singularities appear ubiquitously in wavefields, regardless of the wave equation. Such topological defects are evidenced by wavefront dislocations, as observed in a humongous number ofExpand
Is the continuum SSH model topological?
The discrete Hamiltonian of Su, Schrieffer and Heeger (SSH) [14] is a well-known onedimensional translation-invariant model in condensed matter physics. The model consists of two atoms per unit cellExpand
Chiral edge modes in evolutionary game theory: A kagome network of rock-paper-scissors cycles.
TLDR
It is elucidated that a kagome network of rock-paper-scissors (K-RPS) hosts a chiral edge mode of the population density which is protected by the nontrivial topology in the bulk, which exemplifies the bulk-edge correspondence in two-dimensional systems described by evolutionary game theory. Expand
Berry-Chern monopoles and spectral flows
This lecture note adresses the correspondence between spectral flows, often associated to unidirectional modes, and Chern numbers associated to degeneracy points. The notions of topological indicesExpand
Wave topology brought to the coast
Since the pioneering work of Kelvin on Laplace tidal equations, a zoology of trapped waves have been found in the context of coastal dynamics. Among them, the one originally computed by Kelvin playsExpand
...
1
2
3
...

References

SHOWING 1-10 OF 118 REFERENCES
Proof of the Bulk-Edge Correspondence through a Link between Topological Photonics and Fluctuation-Electrodynamics
The bulk-edge correspondence links the Chern-topological numbers with the net number of unidirectional states supported at an interface of the relevant materials. This fundamental principle isExpand
Bulk-edge correspondence for topological photonic continua
Here, building on our previous work [Phys. Rev. B 92, 125153 (2015)], it is shown that the propagation of unidirectional gapless edge states at an interface of two topologically distinctExpand
Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems
Recently, several authors have investigated topological phenomena in periodically-driven systems of non-interacting particles. These phenomena are identified through analogies between the FloquetExpand
Photonic Floquet topological insulators
TLDR
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. Expand
Bulk–Edge Correspondence for Two-Dimensional Floquet Topological Insulators
Floquet topological insulators describe independent electrons on a lattice driven out of equilibrium by a time-periodic Hamiltonian, beyond the usual adiabatic approximation. In dimension two, suchExpand
Chiral symmetry and bulk{boundary correspondence in periodically driven one-dimensional systems
In periodically driven lattice systems, the effective (Floquet) Hamiltonian can be engineered to be topological; then, the principle of bulk-boundary correspondence guarantees the existence of robustExpand
Bulk-boundary correspondence in three-dimensional topological insulators
We discuss the relation between bulk topological invariants and the spectrum of surface states in three dimensional non-interacting topological insulators. By studying particular models, andExpand
Edge States in Honeycomb Structures
An edge state is a time-harmonic solution of a conservative wave system, e.g. Schrödinger, Maxwell, which is propagating (plane-wave-like) parallel to, and localized transverse to, a line-defect orExpand
Topological non-Hermitian origin of surface Maxwell waves
TLDR
Electromagnetic surface waves, derived from Maxwell theory, underpin many optical effects and applications and are shown to have a topological origin described by the non-Hermitian helicity operator and bulk-boundary correspondence. Expand
Topological kink plasmons on magnetic-domain boundaries
TLDR
This report reports the observation of topologically-protected high-frequency kink modes – kink magnetoplasmons (KMPs) – in a GaAs/AlGaAs two-dimensional electron gas (2DEG) system using custom-shaped strong permanent magnets on top of a Ga as/Al GaAs heterojunction. Expand
...
1
2
3
4
5
...