The progress in the field of topological insulators is impetuous, being sustained by a suite of
exciting results on three fronts: experiment, theory and numerical simulation. Very often, the …

Topological insulators are crystalline solids with supposedly very special properties. If
stumbling upon such a crystal, which is possible because topological insulators are known …

We present examples in three symmetry classes of topological insulators in one or two
dimensions where the proof of the bulk-edge correspondence is particularly simple. This …

Topology plays an increasing role in physics beyond the realm of topological insulators in
condensed mater. From geophysical fluids to active matter, acoustics or photonics, a …

In this article, we study the Schrödinger operator for a large class of periodic potentials with
the symmetry of a hexagonal tiling of the plane. The potentials we consider are …

We analyze the topological properties of systems of Dirac equations in the presence of
heterogeneities to model transport in topological insulators. The topology is described by …

We present the discovery of a novel and intriguing global geometric structure of the (interior)
transmission eigenfunctions associated with the Helmholtz system. It is shown in generic …

An edge state is a time-harmonic solution of a conservative wave system, eg Schrödinger,
Maxwell, which is propagating (plane-wave-like) parallel to, and localized transverse to, a …

Floquet topological insulators describe independent electrons on a lattice driven out of
equilibrium by a time-periodic Hamiltonian, beyond the usual adiabatic approximation. In …

We study one-dimensional insulators obeying a chiral symmetry in the single-particle
picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined …