Compact Localized States in Engineered Flat-Band $\mathcal{P}\mathcal{T}$ Metamaterials

Abstract

The conditions leading to flat dispersionless frequency bands in truly one-dimensional parity-time ($\mathcal{P}\mathcal{T}$) symmetric metamaterials comprising split-ring resonators (SRRs) arranged in a binary pattern are obtained analytically. In this paradigmatic system, in which the SRRs are coupled through both electric and magnetic dipole-dipole forces, flat-bands may arise from tailoring its natural parameters (such as, e.g., the coupling coefficients between SRRs) and not from geometrical effects. For sets of parameters which values are tailored to flatten the upper band of the spectrum, the solution of the corresponding quadratic eigenvalue problem reveals the existence of compact, two-site localized eigenmodes. Numerical simulations confirm the existence and the dynamic stability of such modes, which can be formed through the evolution of single-site initial excitations without disorder or nonlinearity.

to be published in Scientific Reports (2019)

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Cited by in corpus (7)

• Non-Compact Atomic Insulators
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Observation of Flat Frequency Bands at Open Edges and Antiphase Boundary Seams in Topological Mechanical Metamaterials
• Surge of power transmission in flat and nearly flat band lattices
• Corner and Edge States in Topological Sierpinski Carpet Systems
• Topological split-ring resonator based metamaterials with $\mathcal{P}\mathcal{T}$ symmetry relying on gain and loss
• Spin-orbit interactions may relax the rigid conditions leading to flat bands