# Highly degenerate photonic flat bands arising from complete graph configurations

## TL;DR

This paper introduces a novel photonic crystal design inspired by complete graph theory, producing highly degenerate flat bands within a wide frequency range, which are robust against lattice perturbations and enable dispersion-less phenomena.

## Contribution

The work demonstrates a new mechanism for creating highly degenerate flat bands using complete graph configurations, independent of lattice arrangement.

## Key findings

- Flat bands are located in a wide complete 3D bandgap.
- Degeneracy dimension is related to the number of branches of the metallic claw.
- Flat bands are insensitive to lattice perturbations.

## Abstract

Inspired by complete graph theory, we demonstrate that a metallic claw "meta-atom" structure can carry a high number of nearly degenerate resonant modes. A photonic meta-crystal composing of a lattice of such meta-atoms exhibits a large number of flat bands that are squeezed into a narrow frequency window, and these flat bands can be designed to locate in a wide complete 3D bandgap. The degeneracy dimension (Nf) of the flat bands is determined by the number of branches (Nb) of the metallic claw with Nf=Nb-3, which is geometrically related to the complete graph theory. Different from those flat bands emerging from special lattice arrangements (e.g., Kagome lattice), the isolated flat bands here are insensitive to lattice perturbations. The proposed mechanism offers a new platform for realizing various dispersion-less phenomena and a new paradigm to realize high density of states and spectra compressing.

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Source: https://tomesphere.com/paper/1907.00333