Geometry and superfluidity of the flat band in a non-Hermitian optical lattice
Peng He, Hai-Tao Ding, Shi-Liang Zhu
Abstract
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 non-Hermiticity, and the nonreciprocity prominently enhances the phase coherence of the pairing field, suggesting ubiquitous critical behavior of the non-Hermitian fermionic superfluidity.