arXiv subjects

Zhixia Xu

Publications and source records attributed to Zhixia Xu.

5 recordsLinked to original sources

arXiv2025

Nearest-Neighbor Tight-Binding Realization of Hyperbolic Lattices with $\mathbb{Z}_2$ Gauge Structures

A systematic framework for realizing $\mathbb{Z}_2$ gauge extensions of hyperbolic lattices within the nearest-neighbor tight-binding formalism is developed. Using the triangle group $Δ(2,8,8)$ as an example, we classify all inequivalent projective symmetry groups by computing the second cohomology group $H^2(Δ(2,8,8),\mathbb{Z}_2)$. Each class corresponds to a distinct flux configuration and can be constructed by tight-binding models to verify the symmetry relations of the extended group. The translation subgroups of the $\mathbb{Z}_2$ extended lattices are associated with high genus surfaces, which follows the Riemann-Hurwitz formula. By applying the Abelian hyperbolic band theory, we find the all-flat dispersions along specific directions in momentum space and van Hove singularities correlated with discrete eigenenergies. Our results establish a general route to investigate gauge-extended hyperbolic lattices and provide a foundation for further studying symmetry fractionalization and spin liquid phases in non-Euclidean geometries.

physics.optics↗

arXiv2020

Topological valley transport under long-range deformations

Edge states protected by bulk topology of photonic crystals show robustness against short-range disorder, making robust information transfer possible. Here, topological photonic crystals under long-range deformations are investigated. Vertices of each regular hexagon in a honeycomb crystalline structure are shifted randomly to establish a deformed system. By increasing the degree of random deformations, a transition from an ordered system to an amorphous system are investigated, where the close of topological bandgap is clearly shown. We further present comprehensive investigations into excitation methods of the proposed deformed system. Due to the lack of strict periodicity, excitation of topological edge modes becomes difficult. Chiral and linearly polarized sources as two different methods are investigated respectively. It is found that chiral sources are sensitive and rely on the ordered lattice. Even a weak long-range deformation can bring fluctuations to transmission. We further designed and fabricated metal-dielectric-metal sandwich-like samples working in the microwave band. Using linearly polarized source, we detected the existence of topological transport in the deformed system. This work investigates excitation and robustness of bulk topology against long-range deformations and may open the way for exploiting topological properties of materials with a deformed lattice.

physics.optics↗

arXiv2017

Compact bilateral single conductor surface wave transmission line

A compact bilateral single conductor surface wave transmission line (TL) is proposed, converting the quasi-transverse electromagnetic (QTEM) mode of low characteristic impedance slotline into the transverse magnetic (TM) mode of single-conductor TL. The propagation constant of the proposed TL is decided by geometric parameters of the periodic corrugated structure. Compared to conventional transitions between coplanar waveguide (CPW) and single-conductor TLs, such as Goubau line (G-Line) and surface plasmons TL, the proposed structure halves the size and this feature gives important potentials to develop integrated surface wave devices and circuits. The designed structure, sample fabrication and experimental verification are discussed.

physics.app-ph↗

arXiv2007

Rainbow number of matchings in regular bipartite graphs

Given a graph $G$ and a subgraph $H$ of $G$, let $rb(G,H)$ be the minimum number $r$ for which any edge-coloring of $G$ with $r$ colors has a rainbow subgraph $H$. The number $rb(G,H)$ is called the rainbow number of $H$ with respect to $G$. Denote $mK_2$ a matching of size $m$ and $B_{n,k}$ a $k$-regular bipartite graph with bipartition $(X,Y)$ such that $|X|=|Y|=n$ and $k\leq n$. In this paper we give an upper and lower bound for $rb(B_{n,k},mK_2)$, and show that for given $k$ and $m$, if $n$ is large enough, $rb(B_{n,k},mK_2)$ can reach the lower bound. We also determine the rainbow number of matchings in paths and cycles.

math.CO↗

arXiv2007

On the existence of a rainbow 1-factor in proper coloring of K_{rn}^{(r)}

El-Zanati et al proved that for any 1-factorization $\mathcal{F}$ of the complete uniform hypergraph $\mathcal {G}=K_{rn}^{(r)}$ with $r\geq 2$ and $n\geq 3$, there is a rainbow 1-factor. We generalize their result and show that in any proper coloring of the complete uniform hypergraph $\mathcal {G}=K_{rn}^{(r)}$ with $r\geq 2$ and $n\geq 3$, there is a rainbow 1-factor.

math.CO↗