Related papers: Crystallography of Hyperbolic Lattices
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…
One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices…
The emerging possibilities to steer and control electronic motion on subcycle time scales with strong electric fields enable studying the nonperturbative optical response and Bloch bands' topological properties, originated from Berry's…
Hyperbolic lattices extend crystallinity into curved space, where negative curvature and exponentially large boundaries reshape collective excitations beyond Euclidean intuition. In this Letter, we push the study beyond scalar fields by…
Photonic crystals and metamaterials are two overarching paradigms for manipulating light. Combining the two approaches leads to hypercrystals: hyperbolic dispersion metamaterials that undergo periodic modulation and mix…
The celebrated holographic duality posits a correspondence between a quantum gravity in a bulk spacetime and a quantum field theory (QFT) defined on its lower-dimensional boundary. This duality not only offers deep insights into the…
Tight-binding models can accurately replicate the band structure and topology of crystalline systems. They have been widely used in solid-state physics due to their versatility and low computational cost. It is straightforward to build an…
The class of Euclidean unit disk graphs is one of the most fundamental and well-studied graph classes with underlying geometry. In this paper, we identify this class as a special case in the broader class of hyperbolic unit disk graphs and…
Owing to their interesting spectral properties, the synthetic crystals over lattices other than regular Euclidean lattices, such as hyperbolic and fractal ones, have attracted renewed attention, especially from materials and meta-materials…
Liquid crystal elastomers are special cross-linked polymer materials combining the large elastic deformability of elastomers with the orientational orders of liquid crystals. This model exhibits markedly different phenomena than the liquid…
Calculation of band structure of three dimensional photonic crystals amounts to solving large-scale Maxwell eigenvalue problems, which are notoriously challenging due to high multiplicity of zero eigenvalue. In this paper, we try to address…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
To explore the non-Euclidean generalization of higher-order topological phenomena, we construct a higher-order topological insulator model in hyperbolic lattices by breaking the time-reversal symmetry (TRS) of quantum spin Hall insulators.…
The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a…
Discovering the physical requirements for meeting the indefinite permittivity in natural material as well as proposing a new natural hyperbolic media offer a possible route to significantly improve our knowledge and ability to confine and…
Topological solitons are knots in continuous physical fields classified by non-zero Hopf index values. Despite arising in theories that span many branches of physics, from elementary particles to condensed matter and cosmology, they remain…
The topological characteristics of energy bands in crystalline systems are encapsulated in the Berry curvature of the bulk Bloch states. In photonic crystal slabs, far-field emission from guided resonances naturally provides a non-invasive…
We study quantum dynamics of a wave packet on a class of one dimensional decorated aperiodic lattices, described within a tight binding formalism. We look for the possibility of finding extended single particle states even in the absence of…
Tilings of the hyperbolic plane are of significant interest among many branches of mathematics, physics and computer science. Yet, their construction remains a non-trivial task. Current approaches primarily use tree-based recursive…
The percolation transitions on hyperbolic lattices are investigated numerically using finite-size scaling methods. The existence of two distinct percolation thresholds is verified. At the lower threshold, an unbounded cluster appears and…