Geometry and superfluidity of the flat band in a non-Hermitian optical lattice

We propose an ultracold-atom setting where a fermionic superfluidity with attractive s-wave interaction is uploaded in a non-Hermitian Lieb optical lattice. The existence of a real-energy flat band solution is revealed. We show that the interplay between the skin effect and flat-band localization leads to exotic localization properties. We develop a multiband mean-field description of this system and use both order parameters and superfluid weight to describe the phase transition. A relation between the superfluid weight and non-Hermitian quantum metric of the quantum states manifold is built. We find nonmonotone criticality depending on the nonHermiticity, and the nonreciprocity prominently enhances the phase coherence of the pairing field, suggesting ubiquitous critical behavior of the non-Hermitian fermionic superfluidity.

Automated summary

A new ultracold-atom setting is proposed to achieve fermionic superfluidity in a non-Hermitian optical lattice, revealing the existence of flat band solutions and exotic localization properties. The system is described using a multiband mean-field approach, with a relation between superfluid weight and non-Hermitian quantum metric established. Nonmonotone criticality depending on nonHermiticity is found, with nonreciprocity enhancing phase coherence of pairing field, suggesting widespread critical behavior of non-Hermitian fermionic superfluidity.