Aharonov-Bohm Cages in Two-Dimensional Structures

We present an extreme localization mechanism induced by a magnetic field for tight-binding electrons in two-dimensional structures. This original phenomenon is investigated for a large class of tilings (periodic, quasiperiodic, or random). We are led to introduce Aharonov-Bohm cages that are defined as the set of sites eventually visited by a wave packet that can, for particular values of the magnetic flux, be bounded. We finally discuss the quantum dynamics which exhibit an uncommon pulsating behavior.