Flat band induced by the interplay of synthetic magnetic flux and non-Hermiticity

Abstract

A flat band is nondispersive and formed under destructive interference. Although flat bands are found in various Hermitian systems, to realize a flat band in non-Hermitian systems is an interesting task. Here, we propose a flat band in a parity-time symmetric non-Hermitian lattice. The proposed flat band has entirely real energy and is formed at an appropriate match between synthetic magnetic flux and non-Hermiticity. The flat band energy is tunable. At a weak intercell coupling, the flat band is isolated, whereas at a strong intercell coupling, it intersects with the dispersive band at the non-Hermitian phase transition point. The eigenstates of the flat band are compact localized states and are confined in one, two, or three unit cells at the edges or inside the non-Hermitian lattice.

9 pages, 6 figures

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Cited by in corpus (12)

• Flat band in two-dimensional non-Hermitian optical lattices
• Higher-order exceptional point and Landau-Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices
• Geometry and superfluidity of the flat band in a non-Hermitian optical lattice
• Isolated flat bands in an interlocking-circles lattice
• Non-Abelian Aharonov-Bohm Caging in Photonic Lattices
• Stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric flat band lattice
• 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
• Non-Hermitian Aharonov-Bohm Cage
• Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians
• Exceptional flat bands in bipartite non-Hermitian lattices