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Quantum computers require technologies that offer both sufficient control over coherent quantum phenomena and minimal spurious interactions with the environment. We show, that photons confined to photonic crystals, and in particular to…
We propose a nanophotonic platform for topological quantum optics. Our system is composed of a two-dimensional lattice of non-linear quantum emitters with optical transitions embedded in a photonic crystal slab. The emitters interact…
We demonstrate that multiple topological transitions can occur, with high-sensitivity, by continuous change of the geometry of a simple 2D dielectric-frame photonic crystal consisting of circular air-holes. By changing the radii of the…
The rapid development of topological photonics and acoustics calls for accurate understanding of band topology in classical waves, which is not yet achieved in many situations. Here, we present the Wilson-loop approach for exact numerical…
We study topological effects in an one-dimensional plasmonic crystal formed by the screened plasmons emerging in a periodically modulated graphene sheet, placed on top of a metallic substrate. To this end, we develop the theory of…
Crystal symmetries can enforce all bands of a material to be topological, a property that is commonly referred to as ``supertopology". Here, we determine the symmetry-enforced $\mathbb{Z}_2$ supertopologies of non-magnetic centrosymmetric…
Photonic crystals (PCs) with localized optical cavity modes arising from topological domain-wall line defects are simulated for optical biosensing by numerical solution of Maxwell's equations. These consist of a square lattice of square…
The topological characteristics of photonic crystals have been the subject of intense research in recent years. Despite this, the basic question of whether photonic band topology is rare or abundant -- i.e., its relative prevalence --…
A time crystal is a time dependent physical system that does not reach a standstill, even in state of minimum energy. Here we show that the stability of a time crystal can be enhanced by its topology. For this we simulate time crystals made…
The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground state manifold…
Non-Euclidean geometry, discovered by negating Euclid's parallel postulate, has been of considerable interest in mathematics and related fields for the description of geographical coordinates, Internet infrastructures, and the general…
Topological phases usually are unreachable in molecular solids, which are characteristic of weakly dispersed energy bands with a large gap, in contrast to topological materials. In this work, however, we propose that nontrivial electronic…
The field of topological photonics emerged as one of the most promising areas for applications in transformative technologies: possible applications are in topological lasers or quantum optics interfaces. Nevertheless, efficient and simple…
Topological states, first known as quantum Hall effect or Chern insulating crystal, have been generalized to many classical wave systems where potential applications such as robust waveguiding, quantum computing and high-performance lasers…
Topological protection in photonics offers new prospects for guiding and manipulating classical and quantum information. The mechanism of spin-orbit coupling promises the emergence of edge states that are helical; exhibiting unidirectional…
Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in…
Periodically structured materials can sustain both optical and mechanical excitations which are tailored by the geometry. Here we analyze the properties of dispersively coupled planar photonic and phononic crystals: optomechanical crystals.…
Photonic hyper-crystals combine the most interesting features of hyperbolic metamaterials and photonic crystals. Since the dispersion law of extraordinary photons in hyperbolic metamaterials does not exhibit the usual diffraction limit,…
Liquid crystal elastomers and glasses can have significant shape change determined by their director patterns. Cones deformed from circular director patterns have non-trivial Gaussian curvature localised at tips, curved interfaces, and…
Graph representations of solid state materials that encode only interatomic distance lack geometrical resolution, resulting in degenerate representations that may map distinct structures to equivalent graphs. Here we propose a hypergraph…