  In 2015 experiments were performed with superconducting microwave photonic
crystals emulating artificial graphene B. Dietz, T. Klaus, M. Miski-Oglu, and
A. Richter, Phys. Rev. B 91, 035411 (2015)]. The associated density of states
comprises two Dirac points with adjacent bands including van Hove
singularities, thus exhibiting the characteristic features originating from the
extraordinary electronic band structure of graphene. They are separated by a
narrow region of particularly high resonance density corresponding to a nearly
flatband in the band structure, which is reminiscent of that of a honome
lattice -- a combination of two sublattices: honeycomb and kagome. We
demonstrate that, indeed, the density of states, and also the eigenmode
properties and the fluctuations in the resonance-frequency spectra are well
reproduced by a tight-binding model based on the honome lattice. A good
description was achieved by means of the reverse Monte-Carlo approach, thereby
confirming our intepretation of the microwave photonic crystal as an
experimental realization of a honome lattice and providing an answer to
longstanding problem, namely the understanding of the origin of the flatband
bordered by two Dirac points, generally observed in microwave photonic crystals
of different shapes.
