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Quantum electronic transport in flat bands

Résumé :

Over the past decade, we are witnessing a growing interest for the physics in flatband (FB) systems. In these systems and because of destructive quantum interferences the electron group velocity is exactly zero, thus the kinetic energy is quenched. This is at the origin of a plethora of exotic physical phenomena, such as topological states, superconductivity, Wigner crystal and ferromagnetism as well. In standard systems, it is well known that the average intra-band velocity of the carriers at the Fermi energy dictates the quantum transport. This physics is well understood and fully captured within a semi-classical framework. On the other hand, in flat bands, the electronic transport is of quantum nature only. In other words, in contrast to the standard Drude transport, the essence of FB transport cannot be apprehended semi-classically. It will be shown that flat bands sustain an unconventional form of quantum electronic transport of inter-band nature. It is a rather counter intuitive and astonishing feature that a band that consists of localized states exhibits a finite and robust conductivity. In this presentation, I will address the nature of the FB transport in various systems (disordered and nano-patterned) such as graphene, the Lieb lattice, the dice lattice and the Kagomé lattice. It will be shown that the unconventional supermetallicity of the flat bands has a universal character. Thus, a vanishing Drude weight (order parameter of the metal-insulator phase transition) does not systematically imply an insulating phase.