Flat band in two-dimensional non-Hermitian optical lattices

Abstract

We propose a method to generate a real-energy flat band in a two-dimensional (2D) non-Hermitian Lieb lattice. The coincidence of the flat band eigenstate in both real and momentum spaces is essential for the proposed flat band, which is flexible at the appropriate match between the synthetic magnetic flux and non-Hermiticity. The proposed method is not limited to the 2D non-Hermitian Lieb lattice, and is applied to the 2D non-Hermitian Tasaki's decorated square lattice, dice lattice, and kagome lattice. Our findings make a step forward for the flat band engineering in 2D non-Hermitian optical lattices.

arXiv comment8 pages, 4 figures

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• Hybrid exceptional point created from type III Dirac point
• Exceptional points make an astroid in non-Hermitian Lieb lattice: evolution and topological protection
• Geometry and superfluidity of the flat band in a non-Hermitian optical lattice
• Non-Hermitian flatband generator in one dimension
• Isolated flat bands in an interlocking-circles lattice
• Non-Abelian Aharonov-Bohm Caging in Photonic Lattices
• Isolated flat bands in 2D lattices based on a novel path-exchange symmetry
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Tunable Aharonov-Bohm cages through anti-$\mathcal{P}\mathcal{T}$-symmetric imaginary couplings
• Robust incoherent perfect absorption
• Spin-orbit interactions may relax the rigid conditions leading to flat bands
• Exceptional topology in non-Hermitian twisted bilayer graphene
• Exceptional flat bands in bipartite non-Hermitian lattices