From Quantum Geometry to Phase Rigidity in Multiband Superconductors and Exciton Condensates with Enrico Rossi
In multiband systems, the properties of collective states depend not only on the electronic dispersion, but also on the geometry and topology of the Bloch wave functions. I will discuss several manifestations of this principle in excitonic and superconducting systems. I will first introduce the geometric contribution to superfluid weight, using twisted bilayer graphene to illustrate how quantum geometry can sustain phase rigidity of superconducting states even when the electronic bands are nearly flat. I will then show how the quantum metric stabilizes an exciton condensate in double twisted bilayer graphene, reversing the conclusion obtained when geometric contributions to phase fluctuations are neglected. Turning to superconductivity in Haldane phases of chiral two-dimensional electron systems, I will discuss how nontrivial band geometry enhances finite-momentum intravalley pairing over conventional zero-momentum intervalley pairing, favoring a lattice-scale chiral Kekulé superconductivity. Finally, if time permits, I will discuss how disorder suppresses the superfluid weight and how such suppression depends on the band dispersion and quantum geometry.
This lecture was made possible by the William C. Ferguson Fund.