Related papers: Bulk-edge correspondence for nonlinear eigenvalue …

Existing proximity effects stem from systems with a local order parameter, such as a local magnetic moment or a local superconducting pairing amplitude. Here, we demonstrate that despite lacking a local order parameter, topological phases…

Non-Hermitian band theory distinguishes between line gaps and point gaps. While point gaps can give rise to intrinsic non-Hermitian band topology without Hermitian counterparts, line-gapped systems can always be adiabatically deformed to a…

Edge states emerging at the boundaries of materials with nontrivial topology are attractive for many practical applications due to their remarkable robustness to disorder and local boundary deformations, which cannot result in scattering of…

Topological edge states exist at the interfaces between two topologically-distinct materials. The presence and number of such modes are deterministically predicted from the bulk-band topologies, known as the bulk-edge correspondence. This…

For a certain translation invariant tight-binding model of three-dimensional Weyl semimetals, we establish a bulk-edge correspondence as an equality of two relative homology classes, based on an idea of Mathai and Thiang: From spectral…

Topological edge states are known to emerge in certain quasicrystals. We investigate a topological quasicrystal in the presence of nonlinearity by generalizing the Toda lattice to include modulated periodic hoppings, where the period is…

We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping. The system is…

This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic…

We discuss quantum graphs consisting of a compact part and semiinfinite leads. Such a system may have embedded eigenvalues if some edge lengths in the compact part are rationally related. If such a relation is perturbed these eigenvalues…

Some popular mechanisms for restricting the diffusion of waves include introducing disorder (to provoke Anderson localization) and engineering topologically non-trivial phases (to allow for topological edge states to form). However, other…

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 address the co-existence of massless and massive topological edge states at the interface between two materials with different topological phases. We modify the well known Bernevig-Hughes-Zhang model to introduce a smooth function…

We show in the context of Einstein gravity that the removal of a spatial region leads to the appearance of an infinite set of observables and their associated edge states localized at its boundary. Such a boundary occurs in certain…

This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary…

The topology of non-Hermitian systems is fundamentally changed by the non-Hermitian skin effect, which leads to the generalized bulk-boundary correspondence. Based on the non-Bloch band theory, we get insight into the interplay between the…

We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact…

This paper investigates structural changes in the parameters of first-order autoregressive models by analyzing the edge eigenvalues of the precision matrices. Specifically, edge eigenvalues in the precision matrix are observed if and only…

We study topological properties of one-dimensional nonlinear bichromatic superlattices and unveil the effect of nonlinearity on topological states. We find the existence of nontrivial edge solitions, which distribute on the boundaries of…

The bulk-boundary correspondence, which links a bulk topological property of a material to the existence of robust boundary states, is a hallmark of topological insulators. However, in crystalline topological materials the presence of…

We initiate the study of a bulk-boundary eigenvalue problem for the Bilaplacian with a particular third order boundary condition that arises from the study of dynamical boundary conditions for the Cahn-Hilliard equation. First we consider…