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Disordered topological insulators: a non-commutative geometry perspective
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 …
exciting results on three fronts: experiment, theory and numerical simulation. Very often, the …
Bulk and boundary invariants for complex topological insulators
Topological insulators are crystalline solids with supposedly very special properties. If
stumbling upon such a crystal, which is possible because topological insulators are known …
stumbling upon such a crystal, which is possible because topological insulators are known …
The bulk-edge correspondence in three simple cases
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 …
dimensions where the proof of the bulk-edge correspondence is particularly simple. This …
Anomalous bulk-edge correspondence in continuous media
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 …
condensed mater. From geophysical fluids to active matter, acoustics or photonics, a …
Honeycomb Schrödinger operators in the strong binding regime
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 …
the symmetry of a hexagonal tiling of the plane. The potentials we consider are …
Surface-localized transmission eigenstates, super-resolution imaging, and pseudo surface plasmon modes
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 …
transmission eigenfunctions associated with the Helmholtz system. It is shown in generic …
Continuous bulk and interface description of topological insulators
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 …
heterogeneities to model transport in topological insulators. The topology is described by …
Edge states in honeycomb structures
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 …
Maxwell, which is propagating (plane-wave-like) parallel to, and localized transverse to, a …
Bulk–edge correspondence for two-dimensional Floquet topological insulators
Floquet topological insulators describe independent electrons on a lattice driven out of
equilibrium by a time-periodic Hamiltonian, beyond the usual adiabatic approximation. In …
equilibrium by a time-periodic Hamiltonian, beyond the usual adiabatic approximation. In …
The bulk-edge correspondence for disordered chiral chains
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 …
picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined …