Agenda

Résumé : Flat band systems have been the focus of much interest due to the rich exotic physics they display such as non-conventional superconductivity. To study such systems, we developed a multi-band mean field method and showed excellent agreement with exact density matrix renormalization group (DMRG) calculations over a very wide range of parameters and reveal the limits of validity of the simple BCS approach. We design flat band models with tunable topological properties to study the effect of topology, and illustrate the strong dependence of the superconducting density on the compact localized states, rather than being determined by the quantum metric. In addition, we examine the enhancement of superconductivity arising from the band touchings between the flat band and the next dispersive band. Lastly, we investigate superconducting transport in the DC field induced Wannier-Stark flat bands in the presence of interactions. We systematically characterize the superconducting behavior on these flat bands by studying the effect of the DC field and attractive Hubbard interaction strengths on the wavefunction, correlation length, pairing order parameter and the superfluid weight. In particular, we find that the superfluid weight is dramatically enhanced at an optimal value of the interaction strength and weak DC fields.