Related papers: Bulk-edge correspondence for nonlinear eigenvalue …
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, and considering general boundary conditions for the…
The existence of boundary states and their protection against symmetry-preserving perturbations are a hallmark feature of topological systems. While this concept originally emerged in the context of sin-gle-particle phenomena in…
We study a topological field theory in four dimensions on a manifold with boundary. A bulk-boundary interaction is introduced through a novel variational principle rather than explicitly. Through this scheme we find that the boundary values…
Non-Hermitian skin-edge states emerge only at one edge in one-dimensional nonreciprocal chains, where all states are localized at the edge irrespective of eigenvalues. The bulk topological number is the winding number associated with the…
The bulk-boundary correspondence (BBC), i.e. the direct relation between bulk topological invariants defined for infinite periodic systems and the occurrence of protected zero-energy surface states in finite samples, is a ubiquitous and…
Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency…
Topological edge states typically arise at the boundaries of topologically nontrivial structures or at interfaces between regions with differing topological invariants. When topological systems are extended into the nonlinear regime, linear…
Recent studies have extended the notion of band topology to nonlinear systems by defining nonlinear counterparts of eigenvalue problems. They have found the nonlinearity-induced topological transition, while it has required complicated…
The localization is one of the active and fundamental research in topology physics. Based on a generalized Su-Schrieffer-Heeger model with the quasiperiodic non-Hermitian emerging at the off-diagonal location, we propose a novel systematic…
Using the Laughlin's argument on a torus with two pin-holes, we numerically demonstrate that the discontinuities of the center-of-mass work well as an invariant of the pumping phenomena during the process of the flux-attachment, trading the…
We study the two-dimensional rotating shallow-water model describing Earth's oceanic layers. It is formally analogue to a Schr\"odinger equation where the tools from topological insulators are relevant. Once regularized at small scale by an…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
Continuum elasticity is a powerful tool applicable in a broad range of physical systems and phenomena. Yet, understanding how and on what scales material disorder may lead to the breakdown of continuum elasticity is not fully understood. We…
We propose a method to address the existence of topological edge modes in one-dimensional (1D) nonlinearlattices, by deforming the edge modes of linearized models into solutions of the fully nonlinear system. Forlarge enough nonlinearites,…
We study bulk-boundary correspondences and related surface phenomena stabilized by the second Chern number in three-dimensional insulators driven in adiabatic cycles. Magnetic fields and disorder effects are incorporated in our analysis…
For substitutional alloys, typically refered to as classical discrete systems under constant composition, we theoretically examine the role of hidden structure information on evolution of nonlinearity (i.e., correspondence between a set of…
We predict the existence of interaction-driven edge states of bound two-photon quasiparticles in a dimer periodic array of nonlinear optical cavities. Energy spectrum of photon pairs is dramatically richer than in the noninteracting case or…
We investigate the scattering and localization properties of edge and bulk states in a disordered two-dimensional topological insulator when they coexist at the same fermi energy. Due to edge-bulk backscattering (which is not prohibited…
Recently realized higher order topological insulators have taken a surge of interest among the theoretical and experimental condensed matter community. The two-dimensional second order topological insulators give rise to zero-dimensional…
The bulk-boundary correspondence, a topic of intensive research interest over the past decades, is one of the quintessential ideas in the physics of topological quantum matter. Nevertheless, it has not been proven in all generality and has…