Related papers: Bulk-edge correspondence of classical diffusion ph…

Chiral edge states can transmit energy along imperfect interfaces in a topologically robust and unidirectional manner when protected by bulk-boundary correspondence. However, in continuum systems, the number of states at an interface can…

We report on a non-linear scattering effect that challenges the notion of topological protection for wave packets propagating in chiral edge modes. Specifically, in a Floquet topological system close to resonant driving and with a…

The bulk-edge correspondence in topological phases is extended to systems with the generalized chiral symmetry, where the conventional chiral symmetry is broken. In such systems, we find that the edge state exhibits an unconventional…

Bulk-boundary correspondence, a central principle in topological matter relating bulk topological invariants to edge states, breaks down in a generic class of non-Hermitian systems that have so far eluded experimental effort. Here we…

Dislocations are ubiquitous in three-dimensional solid-state materials. The interplay of such real space topology with the emergent band topology defined in reciprocal space gives rise to gapless helical modes bound to the line defects.…

In this paper, we introduce a variation of the notion of topological phase reflecting metric structure of the position space. This framework contains not only periodic and non-periodic systems with symmetries in Kitaev's periodic table but…

An edge state is a time-harmonic solution of a conservative wave system, e.g. Schroedinger, Maxwell, which is propagating (plane-wave-like) parallel to, and localized transverse to, a line-defect or "edge". Topologically protected edge…

We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…

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 is perhaps the most consequential result of…

Topological effects in edge states are clearly visible on short lengths only, thus largely impeding their studies. On larger distances, one may be able to dynamically enhance topological signatures by exploiting the high mobility of edge…

We study edge modes in topological semimetals which have an energy band structure of ordinary semimetals but can be characterized by a Chern number. More specifically, we focus on a Qi-Wu-Zhang-type square-lattice model and a Haldane-type…

Bulk-edge correspondence is a wide-ranging principle that applies to topological matter, as well as a precise result established in a large and growing number of cases. According to the principle, the distinctive topological properties of…

The bulk-edge correspondence predicts that interfaces between topological insulators support robust currents. We prove this principle for PDEs that are periodic away from an interface. Our approach relies on semiclassical methods. It…

Topological theory predicts the necessary conditions for robust dimensional reduction in a host of quantum and classical systems. Models have recently been proposed for stochastic systems which describe many biological and chemical…

In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B…

We show that one-dimensional quasi-periodic optical lattice systems can exhibit edge states and topological phases which are generally believed to appear in two-dimensional systems. When the Fermi energy lies in gaps, the Fermi system on…

Continuum grid-like frames composed of rigidly jointed beams are classic subjects in the field of structural mechanics, whose topological dynamical properties have only recently been revealed. For two-dimensional frames, higher-order…

The bulk-boundary or bulk-edge correspondence is a principle relating surface confined states to the topological classification of the bulk. By combining non-Hermitian ingredients in terms of gain or loss with media that violate…

The puzzling question about the floating of the topological surface state on top of a thick Pb layer, has now possibly been answered. A study of the interface made by Pb on Bi2Se3 for different temperature and adsorbate coverage condition,…

Topological edge states in gaps of non-Hermitian systems are robust due to topological protection. Using the non-Hermitian Floquet Su-Schrieffer-Heeger model, we show that this robustness can break down: edge states may be suppressed by…