STRONG CORRELATIONS AND SUPERCONDUCTIVITY ON THE FLAT BAND

Abstract

In this thesis, we unveil the parameters that control flat band superconductivity by designing and characterizing various dispersionless systems using theoretical and computational methods. We draw comparisons between flat and dispersive bands, and uncover the possibility of significant superconductivity on topologically trivial flat bands. We show that superconductivity on flat bands does not simply depend on its quantum metric, and develop a full multi-band mean field theory to represent accurately the system in regions of different transport mechanisms.

We provide a comprehensive overview and a systematic study on optimizing and enhancing flat band superconductivity with various methods, by controlling the single particle eigenstate, tuning the band gap with lattices we constructed, and even considering another class of systems, the Wannier-Stark flat bands.

Lastly, we investigate the interplay between disorder and interaction on flat bands, and the robustness of flat band superconductivity with respect to the band gap, disorder and interaction strength.