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

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.

10 pages, 4 figures

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• Identifying non-Hermitian critical points with quantum metric
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Pseudospin-orbit coupling and non-Hermitian effects in the Quantum Geometric Tensor of a plasmonic lattice
• Theory of non-Hermitian fermionic superfluidity on a honeycomb lattice: Interplay between exceptional manifolds and van Hove Singularity
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
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• Phase diagram of non-Hermitian BCS superfluids in a dissipative asymmetric Hubbard model
• The global phase diagram of the cluster-XY spin chain with dissipation
• Spin-Depairing-Induced Exceptional Fermionic Superfluidity
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems