Related papers: A Universal Chern Model on Arbitrary Triangulation…
Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite random quadrangulation of this surface with $n$ faces and boundary component lengths of order $\sqrt n$ or of lower order. Endow this…
We develop, from first principles, a general and compact formalism for predicting the electromagnetic response of a metamaterial with non-magnetic inclusions in the long wavelength limit, including spatial dispersion up to the second order.…
This article discusses electromagnetic properties of volumetric metamaterial samples with essentially discrete structure, that is, assembled as a periodic array of electromagnetic resonators. We develop an efficient numerical procedure for…
The search for strong topological phases in generic aperiodic materials and meta-materials is now vigorously pursued by the condensed matter physics community. In this work, we first introduce the concept of patterned resonators as a…
The engineering of topological non-trivial states of matter, using cold atoms, has made great progress in the last decade. Driven by experimental successes, it has become of major interest in the cold atom community. In this work we…
We investigate the possibility of exactly flat non-trivial Chern bands in tight binding models with local (strictly short-ranged) hopping parameters. We demonstrate that while any two of three criteria can be simultaneously realized…
Precise manipulation of the direction and re-direction of vibrational wave energy is a key demand in wave physics and engineering. We consider the paradigm of a finite frame-like structure and the requirement to channel energy away from…
Ultracold atoms in optical lattices form a clean quantum simulator platform which can be utilized to examine topological phenomena and test exotic topological materials. Here we propose an experimental scheme to measure the Chern numbers of…
We analyze a measurement scheme that allows determination of the Berry curvature and the topological Chern number of a Hamiltonian with parameters exploring a two-dimensional closed manifold. Our method uses continuous monitoring of the…
A method is presented for constructing closed surfaces out of Euclidean polygons with infinitely many segment identifications along the boundary. The metric on the quotient is identified. A sufficient condition is presented which guarantees…
Elastic wave manipulation is important in a wide variety of scales in applications including information processing in tiny elastic devices and noise control in big solid structures. The recent emergence of topological materials opens a new…
Motivated by new capabilities to realise artificial gauge fields in ultracold atomic systems, and by their potential to access correlated topological phases in lattice systems, we present a new strategy for designing topologically…
Let N be a topologically finite, orientable 3-manifold with ideal triangulation. We show that if there is a solution to the hyperbolic gluing equations, then all edges in the triangulation are essential. This result is extended to a…
Ultracold atoms trapped in optical superlattices provide a simple platform for realizing the seminal Aubry-Andr\'{e}-Harper (AAH) model. However, the periodic modulations on the nearest-neighbour hoppings have been ignored in this model. In…
Condensed matter systems with topological order and metamaterials with left-handed chirality have attracted recently extensive interests in the fields of physics and optics. So far the two fields are independent, and there is no work to…
Topological edge states in electromagnetic systems feature a set of attracting fundamental properties and unveil prospective applications based on disorder robustness and tailored localization. Despite active efforts in implementing…
This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the…
There are two natural Chern-Simons theories associated with the embedding of a three-dimensional surface in Euclidean space; one is constructed using the induced metric connection -- it involves only the intrinsic geometry, the other is…
Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial…
In spaces of three or more dimensions, there exists topological physics of significant richness that has no lower-dimensional counterparts. To experimentally explore high-dimensional physics, it is advantageous to augment the physical space…