Related papers: Topological Theory for Perfect Metasurface Isolato…
Spectral singularities are ubiquitous with PT-symmetry leading to infinite transmission and reflection coefficients. Such infinities imply the divergence of the fields in the medium thereby breaking the very assumption of the linearity of…
Topological insulators have gapless edge/surface states with novel transport properties. Among these, there are two classes of perfectly conducting channels which are free from backscattering: the edge states of two-dimensional topological…
A systematic analysis of matched layers is undertaken with special attention to better understand the remarkable method of B\'erenger. We prove that the B\'erenger and closely related layers define well posed transmission problems in great…
We develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions. Informally speaking, the obstructions to perfect matchings are geometric, and are of two distinct types: 'space barriers' from convex…
We present an exactly solvable model for one-dimensional symmetry-protected topological phases with $\mathbb{Z}_N\times\mathbb{Z}_N$ symmetry. The model works by binding point topological defects (domain walls) of one symmetry to charges of…
Systems as diverse as mechanical structures assembled from elastic components, and photonic metamaterials enjoy a common geometrical feature: a sublattice symmetry. This property realizes a chiral symmetry first introduced to characterize a…
In this paper we study the asymptotic properties of point configurations that achieve optimal covering of sets lacking smoothness. Our results include the proofs of the existence of asymptotics of best covering and maximal polarization for…
We present a design strategy for selecting the effective polarizability distribution for a metasurface aperture needed to form a desired radiation pattern. A metasurface aperture consists of an array of subwavelength metamaterial elements,…
We define topologically semiperfect (complete, separated, right linear) topological rings and characterize them by equivalent conditions. We show that the endomorphism ring of a module, endowed with the finite topology, is topologically…
Topological insulators constitute one of the most intriguing phenomena in modern condensed matter theory. The unique and exotic properties of topological states of matter allow for unidirectional gapless electron transport and extremely…
In this work, a tensor completion problem is studied, which aims to perfectly recover the tensor from partial observations. The existing theoretical guarantee requires the involved transform to be orthogonal, which hinders its applications.…
We study two-dimensional integrable $N=1$ supersymmetric theories (without topological charges) in the presence of a boundary. We find a universal ratio between the reflection amplitudes for particles that are related by supersymmetry and…
With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral…
We investigate the impact of asymmetric perturbations on the perfect transmission resonances (PTRs) of one-dimensional finite periodic systems. With no perturbations, the scattering region consists of $N$ identical cells, and the…
We report the observation of a novel nonlinear optical response from the prototypical three-dimensional topological insulator Bi$_2$Se$_3$ through the process of high-order harmonic generation. We find that the generation efficiency…
Topological insulators are innovative materials with semiconducting bulk together with surface states forming a Dirac cone, which ensure metallic conduction in the surface plane. Therefore, topological insulators represent an ideal platform…
A relativistic topological insulator model in three spatial dimensions which is a non trivial extension of the non-abelian Landau problem is proposed. The model is exactly soluble and energy levels have both a discrete and a continuous…
In this paper, we study an insulation problem that seeks the optimal distribution of a fixed amount $m>0$ of insulating material coating an insulated boundary $\Gamma_I\subseteq \partial\Omega$ of a thermally conducting body…
An exact solution for electromagnetic wave diffraction at the junction of two-dimensional electron systems (2DES) is obtained and analyzed for electric field polarized along the edge. A special emphasis is paid to the metal-contacted and…
Topology is revolutionizing photonics, bringing with it new theoretical discoveries and a wealth of potential applications. This field was inspired by the discovery of topological insulators, in which interfacial electrons transport without…