Related papers: The polarization problem for the honeycomb structu…
Higher-order topological phase in 2-dimensional (2D) systems is characterized by in-gap corner states, which are hard to detect and utilize. We numerically investigate transport properties of topological corner states in 2D honeycomb…
We establish Schmutz Schaller's conjecture that the hexagonal lattice is `better' than the square lattice. Schmutz Schaller (Bulletin of the AMS 35 (1998), p. 201), motivated by considerations from hyperbolic geometry, conjectured that in…
We study propagation of light in square and hexagonal two-dimensional photonic crystals. We show, that slabs of these crystals focus light with subwavelength resolution. We propose a systematic way to increase this resolution, at an…
In twisted homobilayer transition metal dichalcogenides, intra- and inter-layer valley excitons hybridize with the layer configurations spatially varying in the moir\'e. The ground state valley excitons are trapped at two high-symmetry…
We study the Anderson disordered Hubbard model on the honeycomb lattice. The Hubbard term is han- dled with strong-coupling perturbation theory which encodes the Mott transition physics into a rich dynamical structure of a local…
We discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n, in the limit n -> oo, d -> oo, d/n=delta. The problem is relevant for coding theory. We find a solution to the…
In this article we investigate the $N$-point min-max and the max-min polarization problems on the sphere for a large class of potentials in $\mathbb{R}^n$. We derive universal lower and upper bounds on the polarization of spherical designs…
We report on the experimental observation of two-dimensional surface solitons residing at the interface between a homogeneous square lattice and a superlattice that consists of alternating "deep" and "shallow" waveguides. By exciting single…
We have investigated the growth of Pt on Ge(110) using scanning tunneling microscopy and spectroscopy. The deposition of several monolayers of Pt on Ge(110) followed by annealing at 1100 K results in the formation of three-dimensional…
We study the possible superconducting pairing symmetry mediated by spin and charge fluctuations on the honeycomb lattice using the extended Hubbard model and the random-phase-approximation method. From $2\%$ to $20\%$ doping levels, a…
We present a study of radiation propagation through disordered amplifying honeycomb photonic lattice, where elastic scattering provides feedback for light generation. To explore the interplay of different scattering mechanisms and the…
Photonic modes exhibiting a polarization winding akin to a vortex possess an integer topological charge. Lasing with topological charge 1 or 2 can be realized in periodic lattices of up to six-fold rotational symmetry. Higher order charges…
In this paper we prove an analogue of Mordell's inequality for lattices in finite-dimensional complex or quaternionic Hermitian space that are modules over a maximal order in an imaginary quadratic number field or a totally definite…
We consider an ultra-small system of polarized bosons on an optical lattice with a ring topology interacting via long range dipole-dipole interactions. Dipoles polarized perpendicular to the plane of the ring reveal sharp transitions…
A novel model, devised to describe spontaneous chirality synchronization in complex liquids and liquid crystals, is proposed and studied. Segments of ribbon-like molecular columns with left- or right-handed 180degree twist lie on the bonds…
We study the ground state properties of repulsively interacting bosons on the honeycomb lattice using large-scale quantum Monte Carlo simulations. In the hard-core limit the half-filled system develops long ranged diagonal order for…
We report the discovery of weak topological insulators by ab initio calculations in a honeycomb lattice. We propose a structure with an odd number of layers in the primitive unit-cell as a prerequisite for forming weak topological…
We investigate a new kind of dark solitons and vortices that can exist in the exciton-polariton condensates. These structures have discontinuity in the excitonic part of the polaritonic field and exist due to an intrinsic multiplicity of…
We construct a minimal four-band model for the two-dimensional (2D) topological insulators and quantum anomalous Hall insulators based on the $p_x$- and $p_y$-orbital bands in the honeycomb lattice. The multiorbital structure allows the…
The electrostatics of 2D system with complicated inner boundary is studied. The object which we call "monster" is built by an iterative process of multiple conformal mapping of the circle exterior. The procedure leads to the figures built…