Diamagnetic Response due to Localization in Chains of Connected Mesoscopic Rings

A dynamic response to a magnetic field of a chain of connected mesoscopic rings is considered. We show that the low frequency behavior corresponds to localization of the elctrons along the chain and to diamagnetic dynamic currents inside rings. The magnetization density due to these currents does not vanish even in the limit of the infinitely long chain of strongly connected rings. showing that this is a macroscopic effect. Being of a dynamic origin the currents can be destroyed by inelastic scattering, but we argue that the corresponding decay time can at low enough temperatures be large compared to all other time scales of the system. We suggest to check our results by measuring the magnetization of an ensemble of chains of connected rings in the diffusive regime or alternatively of linear antidot lattices where the mean free path due to elastic scattering is smaller than the superlattice spacing. This yields a new contactless method of studying the localization.