相关论文: High contrast elliptic operators in honeycomb stru…

We present full description of spectra for a Hamiltonian defined on periodic hexagonal elastic lattices. These continua are constructed out of Euler-Bernoulli beams, each governed by a scalar-valued self-adjoint operator, which is also…

Given an open set $\Omega\subset\mathbb{R}^3$. We deal with the spectral study of Dirac operators of the form $H_{a,\tau}=H+A_{a,\tau}\delta_{\partial\Omega}$, where $H$ is the free Dirac operator in $\mathbb{R}^3$, $A_{a,\tau}$ is a…

This paper is devoted to the approximation of two and three-dimensional Dirac operators $H_{\widetilde{V} \delta_\Sigma}$ with combinations of electrostatic and Lorentz scalar $\delta$-shell interactions in the norm resolvent sense. Relying…

Moving, merging and annihilating Dirac points are studied theoretically in the tight-binding model on honeycomb lattice with up-to third-nearest-neighbor hoppings. We obtain a rich phase diagram of the topological phase transitions in the…

We study wave propagation in 2D honeycomb structures with a non-commensurate or ``irrational'' line defect or edge. Our model is a Schr\"odinger operator which interpolates, across the edge, between two distinct bulk (asymptotic)…

In a recent article [10], the authors proved that the non-relativistic Schr\"odinger operator with a generic honeycomb lattice potential has conical (Dirac) points in its dispersion surfaces. These conical points occur for quasi-momenta,…

Two-dimensional (2D) coupled resonant optical waveguide (CROW), exhibiting topological edge states, provides an efficient platform for designing integrated topological photonic devices. In this paper, we propose an experimentally feasible…

The spectrum of tight binding electrons on a square lattice with half a magnetic flux quantum per unit cell exhibits two Dirac points at the band center. We show that, in the presence of an additional uniaxial staggered potential, this pair…

The honeycomb lattice sets the basic arena for numerous ideas to implement electronic, photonic, or phononic topological bands in (meta-)materials. Novel opportunities to manipulate Dirac electrons in graphene through band engineering arise…

One of key challenges in current material research is to search for new topological materials with inverted bulk-band structure. In topological insulators, the band inversion caused by strong spin-orbit coupling leads to opening of a band…

We consider the two-dimensional Dirac operator with Lorentz-scalar $\delta$-shell interactions on each edge of a star-graph. An orthogonal decomposition is performed which shows such an operator is unitarily equivalent to an orthogonal sum…

We give a Riemannian structure to the set $\Sigma$ of positive invertible unitized Hilbert-Schmidt operators, by means of the trace inner product. This metric makes of $\Sigma$ a nonpositively curved, simply connected and metrically…

Let $(M,g)$ be a closed, smooth, Riemannian manifold of dimension $m \geq 1$. Let $\eta$ be a smooth $(0,1)$-tensor field on $M$. The divergence of $\eta$ is defined as $\text{div}_g(\eta):=g^{ij}(\nabla \eta)_{ij}$. Now let $\Delta_g$ be a…

Gyroscopic metamaterials --- mechanical structures composed of interacting spinning tops --- have recently been found to support one-way topological edge excitations. In these structures, the time reversal symmetry breaking that enables…

We examine spectra of Dirac operators on compact hyperbolic surfaces. Particular attention is devoted to symmetry considerations, leading to non-trivial multiplicities of eigenvalues. The relation to spectra of Maass-Laplace operators is…

We define Dirac operators on $\mathbb{S}^3$ (and $\mathbb{R}^3$) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among…

The theory of self-adjoint extensions of first and second order elliptic differential operators on manifolds with boundary is studied via its most representative instances: Dirac and Laplace operators. The theory is developed by exploiting…

We present new results on the block-diagonalization of Dirac operators on three-dimensional Euclidean space with unbounded potentials. Classes of admissible potentials include electromagnetic potentials with strong Coulomb singularities and…

In this paper we study the asymptotic behaviour as $\varepsilon\to 0$ of the spectrum of the elliptic operator $\mathcal{A}^\varepsilon=-{1\over b^\varepsilon}\mathrm{div}(a^\varepsilon\nabla)$ posed in a bounded domain…

We reexamine the existence and stability conditions of Dirac points between valence and conduction bands of 3/4 filled $\alpha$-(BEDT-TTF)$_2$I$_3$ conducting plane. We consider the usual nearest neigbhor tight binding model with the seven…