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Collective electronic transport close to the metal-insulator or superconductor insulator transitions.

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Mathematics and Physics of Anderson localization: 50 Years After

Insulators close to the transition to a metal or a superconductor exhibit interesting collective electronic phenomena which are prominently reflected in transport properties. An important feature in systems close to the metal-insulator transition is the apparently purely electronic nature of activated transport seen in experiments. This does not fit into the standard theory of phonon-assisted hopping conduction and has remained an unexplained puzzle for decades. It also seems to contradict recent theories of many body localization (localization in the Fock space of interacting systems), which have predicted a finite temperature metal insulator transition for interacting, Anderson localized electrons. I will address this problem for Anderson insulators with a single-particle localization length much larger than the mean distance between electrons. I will argue that under these circumstances Coulomb interactions drive the electrons into a strongly correlated quantum glass phase with a gapless spectrum of delocalized collective excitations which act as a bath with which individual electrons can exchange energy. However, the same reasoning does not necessarily apply close to a insulator-to-superconductor transition, where electrons are bound into preformed Cooper pairs and Coulomb interactions are weak. I will argue that these systems are promising candidates to exhibit strong remnants of many body localization, which may be the key to an explanation for their unusual transport properties.

This talk is part of the Isaac Newton Institute Seminar Series series.

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