Non-Hermitian lattices with a flat band and polynomial power increase

Abstract

In this work we first discuss systematically three general approaches to construct a non-Hermitian flat band, defined by its dispersionless real part. They resort to, respectively, spontaneous restoration of non-Hermitian particle-hole symmetry, a persisting flat band from the underlying Hermitian system, and a compact Wannier function that is an eigenstate of the entire system. For the last approach in particular, we show the simplest lattice structure where it can be applied, and we further identify a special case of such a flat band where every point in the Brillouin zone is an exceptional point of order 3. A localized excitation in this "EP3 flat band" can display either a conserved power, quadratic power increase, or even quartic power increase, depending on whether the localized eigenstate or one of the two generalized eigenvectors is initially excited. Nevertheless, the asymptotic wave function in the long time limit is always given by the eigenstate, and in this case, the compact Wannier function or its superposition in two or more unit cells.

7 pages, 9 figures

References in corpus (11)

• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Visualization of Branch Points in PT-Symmetric Waveguides
• Observation of a localized flat-band state in a photonic Lieb lattice
• Observation of bound states in Lieb photonic lattices
• Topological flat band models with arbitrary Chern numbers
• Flat Bands Under Correlated Perturbations
• Asymmetric scattering and non-orthogonal mode patterns in optical micro-spirals
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• Exceptional points and lasing self-termination in photonic molecules
• Symmetry-protected zero-mode laser with a tunable spatial profile

Cited by in corpus (29)

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• Optical Lattices with Higher-order Exceptional Points by Non-Hermitian Coupling
• Flat band in two-dimensional non-Hermitian optical lattices
• Photonic Flatband Laser
• Higher-order exceptional point and Landau-Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices
• Flat band induced by the interplay of synthetic magnetic flux and non-Hermiticity
• Geometry and superfluidity of the flat band in a non-Hermitian optical lattice
• Imaginary gauge transformation in momentum space and Dirac exceptional point
• Chiral symmetry in non-Hermitian systems: product rule and Clifford algebra
• Non-Hermitian flatband generator in one dimension
• Unitary Scattering Protected by Pseudo-Hermiticity
• Dissipation Induced Flat Bands
• Non-singular and singular flat bands in tunable acoustic metamaterials
• Analysis of Dirac exceptional points and their isospectral Hermitian counterparts
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation
• Tunable Aharonov-Bohm cages through anti-$\mathcal{P}\mathcal{T}$-symmetric imaginary couplings
• Non-Hermitian gauged laser arrays with localized excitations: Anomalous threshold and generalized principle of selective pumping
• Robust incoherent perfect absorption
• Linear localization of zero modes in weakly coupled non-Hermitian reservoirs
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Emergent localized states at the interface of a twofold $\mathcal{P}\mathcal{T}$-symmetric lattice
• Origin of robust exceptional points: a restricted bulk zero mode
• Non-Hermitian systems with a real spectrum and selective skin effect
• Effective size of a parity-time symmetric dimer
• Observing complementary Lucas sequences using non-Hermitian zero modes