Parity-time symmetry in a flat band system

Abstract

In this paper we introduce Parity-Time ($\mathcal{P}\mathcal{T}$) symmetric perturbation to a one-dimensional Lieb lattice, which is otherwise $\mathcal{P}$-symmetric and has a flat band. In the flat band there are a multitude of degenerate dark states, and the degeneracy $N$ increases with the system size. We show that the degeneracy in the flat band is completely lifted due to the non-Hermitian perturbation in general, but it is partially maintained with the half-gain-half-loss perturbation and its ``V" variant that we consider. With these perturbations, we show that both randomly positioned states and pinned states at the symmetry plane in the flat band can undergo thresholdless $\mathcal{P}\mathcal{T}$ breaking. They are distinguished by their different rates of acquiring non-Hermicity as the $\mathcal{P}\mathcal{T}$-symmetric perturbation grows, which are insensitive to the system size. Using a degenerate perturbation theory, we derive analytically the rate for the pinned states, whose spatial profiles are also insensitive to the system size. Finally, we find that the presence of weak disorder has a strong effect on modes in the dispersive bands but not on those in the flat band. The latter respond in completely different ways to the growing $\mathcal{P}\mathcal{T}$-symmetric perturbation, depending on whether they are randomly positioned or pinned.

8 pages, 8 figures

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• Realization of robust boundary modes and non-contractible loop states in photonic Kagome lattices
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• $\mathcal{P}\mathcal{T}$-symmetric wave guide system with evidence of a third-order exceptional point
• Experimental realisation of $\mathcal{P}\mathcal{T}$-symmetric flat bands
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• Flat bands and PT-symmetry in quasi-one-dimensional lattices
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• Higher-order exceptional point in a blue-detuned non-Hermitian cavity optomechanical system
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• Pseudo-chirality: a manifestation of Noether's theorem in non-Hermitian systems
• Flat bands and compactons in mechanical lattices
• Interplay of quantum phase transition and flat band in hybrid lattices
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• Compact Localized States in Engineered Flat-Band $\mathcal{P}\mathcal{T}$ Metamaterials
• On Stability of Flat Band Modes in a Rhombic Nonlinear Optical Waveguide Array
• Characterization of Parity-Time Symmetry in Photonic Lattices Using Heesh-Shubnikov Group Theory
• Optical fluxes in coupled $\mathcal{P}\mathcal{T}$-symmetric photonic structures
• Analysis of Dirac exceptional points and their isospectral Hermitian counterparts
• Comprehensive understanding of parity-time transitions in $\mathcal{P}\mathcal{T}$ symmetric photonic crystals with an antiunitary group theory
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Effects of non-uniform distributions of gain and loss in photonic crystals
• Simple models of three coupled $\mathcal{P}\mathcal{T}$-symmetric wave guides allowing for third-order exceptional points
• Non-Hermitian gauged laser arrays with localized excitations: Anomalous threshold and generalized principle of selective pumping
• Robust incoherent perfect absorption
• Emergent localized states at the interface of a twofold $\mathcal{P}\mathcal{T}$-symmetric lattice
• Non-diffracting states at exceptional points
• Reconfiguration of quantum states in $\mathcal{P}T$-symmetric quasi-one dimensional lattices
• Origin of robust exceptional points: a restricted bulk zero mode
• Exceptional topology in non-Hermitian twisted bilayer graphene
• Non-Hermitian Aharonov-Bohm Cage
• Landau-Zener transitions through a pair of higher order exceptional points
• Observing complementary Lucas sequences using non-Hermitian zero modes