Résumé : Over the past years, we have been witnessing a rapidly growing interest for the physics in flat-band (FB) systems. FBs are dispersionless parts in the electronic spectrum originating from destructive quantum interferences. FBs are at the heart of a plethora of exotic and unexpected physical phenomena, such as topological states, unconventional superconductivity, and Wigner crystals. In this presentation, I illustrate several intriguing and counter-intuitive features associated with the physics of flat bands in two-dimensional systems. I will first discuss the impact of FBs on quantum electronic transport in various 2D systems. I will show that the unconventional conductivity in FBs can be directly linked to the quantum metric (QM) of the FB eigenstates, thus revealing the geometric nature of this unusual form of quantum transport.
I will show as well that disorder can boost the QM by orders of magnitude and that this could have a significant impact on superconductivity. Finally, as the possibility of long-range ferromagnetic ordering in 2D materials is currently generating a growing excitement, it will be demonstrated that FBs could pave a pathway to room temperature ferromagnetism in 2D magnetic materials.
