Related papers: Geometry and Topological photonics
This is an exposition of results on the existence problem of $\pi_1$-injective immersed and embedded surfaces in graph-manifolds, and also of nonpositively curved metrics on graph-manifolds, obtained by different authors. The results are…
Topological states enable robust transport within disorder-rich media through integer invariants inextricably tied to the transmission of light, sound, or electrons. However, the challenge remains to exploit topological protection in a…
The integration of topology into photonics has generated a new design framework for constructing robust and unidirectional waveguides, which are not feasible with traditional photonic devices. Here, we overcome current barriers to the…
The proposition that photon is a topological object (J. Math. Phys. 49, 032303, 2008) is given rigorous foundation based on pure vector field theory independent of the electromagnetic fields. Holomorphy of 4-dimensional space-time and the…
Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topological order. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators…
The study of band topology in photonic crystals was primarily focused on near-field effects, including edge states and high order corner states. However, this work investigated the polarization distribution of radiated fields for photonic…
Topological insulators in three dimensions are nonmagnetic insulators that possess metallic surface states as a consequence of the nontrivial topology of electronic wavefunctions in the bulk of the material. They are the first known…
Topology describes properties of physical systems that remain constant under continuous deformations. For infinite vector waves, global topological invariants in position space are typically associated with periodic patterns. We demonstrate…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
Topology forms a cornerstone in modern condensed matter and statistical physics, offering a new framework to classify the phases and phase transitions beyond the traditional Landau paradigm. However, it is widely believed that topological…
Topological photonics sheds light on some of the surprising phenomena seen in condensed matter physics that arise with the appearance of topological invariants. Optical waveguides provide a well-controlled platform to investigate effects…
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
Topological insulators are innovative materials with semiconducting bulk together with surface states forming a Dirac cone, which ensure metallic conduction in the surface plane. Therefore, topological insulators represent an ideal platform…
Carbon nanotube Y-junctions are of great interest to the next generation of innovative multi-terminal nanodevices. Topological indices are graph-theoretically based parameters that describe various structural properties of a chemical…
We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…
We describe the second integral cohomology group of a surface bundle as the group of Chern classes of fiberwise holomorphic complex line bundles and use this to obtain information on this group.
Topology is central to phenomena that arise in a variety of fields, ranging from quantum field theory to quantum information science to condensed matter physics. Recently, the study of topology has been extended to open systems, leading to…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
Topological states of light represent counterintuitive optical modes localized at boundaries of finite-size optical structures that originate from the properties of the bulk. Being defined by bulk properties, such boundary states are…
Topological states of light represent counterintuitive optical modes localized at boundaries of finite-size optical structures that originate from the properties of the bulk. Being defined by bulk properties, such boundary states are…