Related papers: Analytic bulk-edge connection in circular-symmetri…
With the inclusion of arbitrary long-range hopping and (pseudo)spin-orbit coupling amplitudes, we formulate a generic model that can describe any two-dimensional two-band bulk insulators, thus providing a simple framework to investigate…
We rigorously yet concisely prove the bulk-edge correspondence for general $d$-dimensional ($d$D) topological insulators in complex Altland-Zirnbauer classes, which states that the bulk topological number equals to the edge-mode index.…
A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting…
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…
Anomalous topological phases, where edge states coexist with topologically trivial Chern bands, can only appear in periodically driven lattices. When the driving is smooth and continuous, the bulk-edge correspondence is guaranteed by the…
Despite the extensive studies of topological states, their characterization in strongly nonlinear classical systems has been lacking. In this work, we identify the proper definition of Berry phase for nonlinear bulk modes and characterize…
Intriguing issues in one-dimensional non-reciprocal topological systems include the breakdown of usual bulk-edge correspondence and the occurrence of half-integer topological invariants. In order to understand these unusual topological…
Topological edge modes are excitations that are localized at the materials' edges and yet are characterized by a topological invariant defined in the bulk. Such bulk-edge correspondence has enabled the creation of robust electronic,…
Topological insulators in three spatial dimensions are known to possess a precise bulk/boundary correspondence, in that there is a one-to-one correspondence between the 5 classes characterized by bulk topological invariants and Dirac…
The bulk-edge correspondence for topological quantum liquids states that the spectrum of the reduced density matrix of a large subregion reproduces the thermal spectrum of a physical edge. This correspondence suggests an intricate…
The Zak phase $\gamma$, the generalization of the Berry phase to Bloch wave functions in solids, is often used to characterize inversion-symmetric 1D topological insulators; however, since its value can depend on the choice of real-space…
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. This work introduces bispectral mode decomposition as a direct means of educing flow structures that are associated with triadic interactions from…
This paper concerns the topological classification of continuous Hamiltonians that find applications in biased cold plasmas and photonics. Besides a magnetic bias, the Hamiltonians are parametrized by a plasma frequency and a fixed vertical…
We describe the formation of bulk and edge arcs in the dispersion relation of two-dimensional coupled-resonator arrays that are topologically trivial in the hermitian limit. Each resonator provides two asymmetrically coupled internal modes,…
When two topologically trivial and nontrivial systems are brought together, a localized energy state is formed at the interface. For crystalline quantum and classical systems, their topology can be determined by studying the eigenmode…
We examine statistical fluctuation of eigenvalues from the near-edge bulk of QCD Dirac spectra above the critical temperature. For completeness we start by reviewing on the spectral property of Anderson tight-binding Hamiltonians as…
Topological photonics is developed based on the analogy of Schr\"{o}dinger equation which is mathematically reduced to a standard eigenvalue equation. Notably, several photonic systems are beyond the standard topological band theory as they…
The Dirac operator provides a unified framework for processing signals defined over different order topological domains, such as node and edge signals. Its eigenmodes define a spectral representation that inherently captures cross-domain…
Using previous results from boundary conformal field theory and integrability, a phase diagram is derived for the 2 dimensional Ising model at its bulk tri-critical point as a function of boundary magnetic field and boundary spin-coupling…
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…