This paper reviews recent results on the classification of partial differential operators
modeling bulk and interface topological insulators in Euclidean spaces. Our main objective …

This book is a synthesis of recent advances in the spectral theory of the magnetic
Schrödinger operator. It can be considered a catalog of concrete examples of magnetic …

This paper proposes a classification of elliptic (pseudo-) differential Hamiltonians describing
topological insulators and superconductors in Euclidean space by means of domain walls …

Both the physics and applications of fermionic symmetry-protected topological phases rely
heavily on a principle known as bulk-boundary correspondence, which predicts the …

We complete the analysis of the band functions for two-dimensional magnetic Schrödinger
operators with piecewise constant magnetic fields. The discontinuity of the magnetic field …

We analyze the propagation of two-dimensional dispersive and relativistic wavepackets
localized in the vicinity of the zero level set of a slowly varying domain wall modeling the …

We analyze the 2D magnetic Laplacian in the semiclassical limit in the case when the
magnetic field vanishes along a smooth curve. In particular, we prove local and micro-local …

In the tight-binding approximation, an Iwatsuka magnetic field is modeled by a function on
$\mathbb {Z}^ 2$ with constant, but distinct values in the two parts of the lattice separated by …

At the interface of two two-dimensional quantum systems, there may exist interface currents
similar to edge currents in quantum Hall systems. It is proved that these interface currents …

We study the propagation of currents along the interface of two $2 $-$ d $ magnetic systems,
where one of them occupies the first quadrant of the plane. By considering the tight-binding …