Related papers: Edge states for second order elliptic operators in…
We apply the iterated edge state tracking algorithm to study the boundary between laminar and turbulent dynamics in plane Couette flow at Re=400. Perturbations that are not strong enough to become fully turbulent nor weak enough to…
A honeycomb array of helical waveguides with zigzag-zigzag edges and a refractive index gradient orthogonal to the edges may support Floquet bound states in continuum (BICs). The gradient of the refractive index leads to strong asymmetry of…
This paper investigates realisations of elliptic differential operators of general order on manifolds with boundary following the approach of B\"ar-Ballmann to first order elliptic operators. The space of possible boundary values of…
A two-dimensional quadrupole topological insulator on a square lattice is a typical example of a higher-order topological insulator. It hosts an edge state localized near each of its $90^{\circ}$ corners at an energy $E$ inside the band…
We study extensions of the mappings arising in usual channel-state duality to the case of Hilbert spaces with a direct sum structure. This setting arises in representations of algebras with centers, which are commonly associated with…
We consider the geometry of second order linear operators acting on the commutative algebra of densities on a (super)manifold introduced in our previous work. In the conventional language, operators on the algebra of densities correspond to…
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
The model problem of a plane angle for a second-order elliptic system subject to Dirichlet, mixed, and Neumann boundary conditions is analyzed. For each boundary condition, the existence of solutions of the form $r^\lambda v$ is reduced to…
Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each…
The bulk-edge correspondence in topological phases is extended to systems with the generalized chiral symmetry, where the conventional chiral symmetry is broken. In such systems, we find that the edge state exhibits an unconventional…
Energies and wave functions of edge states in twodimensional electron gas are evaluated for a finite step potential barrier model. The spectrum exhibits richer structure than observed previously for an infinite barrier model. Surprisingly,…
Here, we report experimental evidence suggesting the emergence of robust, possibly chiral, edge states in artificially engineered multilayers composed of alternating nanometer-thick layers of nonmagnetic aluminum (Al) and ferromagnetic…
We examine the properties of edge states in a two-dimensional topological insulator. Based on the Kane-Mele model, we derive two coupled equations for the energy and the effective width of edge states at a given momentum in a semi-infinite…
We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open…
For 2D topological insulators with strong electron-hole hybridization, such as HgTe/CdTe quantum wells, the widely used 4 x 4 k.p Hamiltonian based on the first electron and heavy hole sub-bands yields an equal number of physical and…
We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However,…
We study and classify the emergence of protected edge modes at the junction of one-dimensional materials. Using symmetries of Lagrangian planes in boundary symplectic spaces, we present a novel proof of the periodic table of topological…
We consider the emergence of edge states in a finite optical lattice and show that the boundaries of the lattice play a decisive role for their location in the corresponding energy spectrum. We introduce a simple parametrisation of the…
We give necessary and sufficient conditions for the solvability of some semilinear elliptic boundary value problems involving the Laplace operator with linear and nonlinear highest order boundary conditions involving the Laplace-Beltrami…
We study the interplay between two nontrivial boundary effects: (1) the two dimensional ($2d$) edge states of three dimensional ($3d$) strongly interacting bosonic symmetry protected topological states, and (2) the boundary fluctuations of…