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

TL;DR

This paper explores a non-Hermitian optical lattice system with flat bands, revealing unique localization and superfluid properties influenced by non-Hermiticity and skin effects, and establishing a link between superfluid weight and quantum metric.

Contribution

It introduces a multiband mean-field framework for non-Hermitian superfluidity, highlighting the role of quantum geometry and non-reciprocity in phase transitions.

Findings

Existence of real-energy flat band in non-Hermitian lattice

Non-monotonic criticality influenced by non-Hermiticity

Enhanced phase coherence due to non-reciprocity

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 non-monotone criticality depending on the non-Hermiticity, and the non-reciprocity prominently enhances the phase coherence of the pairing field, suggesting ubiquitous critical behavior of the non-Hermitian fermionic superfluidity.