Related papers: Optical Quasi-symmetry Groups for Meron Lattices

Photonic skyrmion and meron lattices are structured light fields with topologically protected textures, analogous to magnetic skyrmions and merons. Here, we report the theoretical existence of mixed skyrmion and meron quasicrystals in an…

The crystal symmetry of a material dictates the type of topological band structures it may host, and therefore symmetry is the guiding principle to find topological materials. Here we introduce an alternative guiding principle, which we…

Symmetry invariants of a group specify the classes of quasiparticles, namely the classes of projective irreducible co-representations in systems having that symmetry. More symmetry invariants exist in discrete point groups than the full…

Optical skyrmions formed in terms of polarization are topological quasi-particles and have garnered much interest in the optical community owing to their unique inhomogeneous polarization structure and simplicity in their experimental…

Symmetry governs many electronic and photonic phenomena in optics and condensed matter physics. Skyrmions and merons are prominent topological structures in magnetic materials, with the topological features determined by the interplay…

Symmetry formulated by group theory plays an essential role with respect to the laws of nature, from fundamental particles to condensed matter systems. Here, by combining symmetry analysis and tight-binding model calculations, we elucidate…

Emergent quasiparticles in solids often exhibit unique topological properties as a result of the complex interplay between charge, orbital, spin and lattice degrees of freedom. Among these quasiparticles, the polaron occupies a special…

The discovery of quasicrystals with crystallographically forbidden rotational symmetries has changed the notion of the ordering in materials, yet little is known about the dynamical emergence of such exotic forms of order. Here we…

Quantum nonlinear optics is a quickly growing field with large technological promise, at the same time involving complex and novel many-body phenomena. In the usual scenario, optical nonlinearities originate from the interactions between…

Topological defects are pivotal in elucidating kaleidoscopic topological phenomena in different physical systems. Meron-antimeron pairs are a type of topological defects firstly found as soliton solutions to SU(2) Yang-Mills equations in…

A lattice symmetry, if being nonsymmorphic, is defined by combining a point group symmetry with a fractional lattice translation that cannot be removed by changing the lattice origin. Nonsymmorphic symmetry has a substantial influence on…

In this note, we announce the first results on quasi-isometric rigidity of non-nilpotent polycyclic groups. In particular, we prove that any group quasi-isometric to the three dimenionsional solvable Lie group Sol is virtually a lattice in…

The two discrete generators of the full Lorentz group $O(1,3)$ in $4D$ spacetime are typically chosen to be parity inversion symmetry $P$ and time reversal symmetry $T$, which are responsible for the four topologically separate components…

The interaction between a photon and a qubit in the Janeys-Cummings (JC) model generates a kind of quasiparticle called polariton. While they are widely used in quantum optics, difficulties in engineering controllable coupling of them…

We define a notion of a rotund quasi-uniform space and describe a new direct construction of a (right-continuous) quasi-pseudometric on a (rotund) quasi-uniform space. This new construction allows to give alternative proofs of several…

Topological quasiparticles such as skyrmions and merons have recently attracted enormous attentions in the form of diverse optical degrees of freedom. However, these structures have not been explored in the fundamental momentum vectors of…

It is known that two coupled harmonic oscillators can support the symmetry group as rich as O(3,3) which corresponds to the Lorentz group applicable to three space-like and three time-like coordinates. This group contains many subgroups,…

When studying mirror symmetry in the context of K3 surfaces, the hyperkaehler structure of K3 makes the notion of exchanging Kaehler and complex moduli ambiguous. On the other hand, the metric is not renormalized due to the higher amount of…

We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of equal rank, higher rank symmetric spaces are close to isometric embeddings. We also produce some surprising examples of quasi-isometric…

Skyrmions are topologically stable quasiparticles that have been predicted and demonstrated in quantum fields, solid-state physics, and magnetic materials, but only recently observed in electromagnetic fields, triggering fast expanding…