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We study theoretically and numerically high density of states for hyperbolic bilayered metamaterials (HMM). It reveals that density response of HMMis reminiscent of Fermi electronic band structure of metal or semiconductors. By the method of Green function a van Hove type singularity is found in photonic density spectra of HMM with saddle
point localization on photonic Fermi surface (FS) of metamaterial Similar to the electronic systems, the photonic FS
close to Van Hove singularity experiences instabilities induced by the changes in volume fractions of its constituents
that leads to the Lifshitz type zero-temperature phase transition between FS of types I and II hyperbolic states at the
protected by topology critical point.
Vitally Pustovit,David Zelmon,Kurt Eyink, andAugustine Urbas
"A Van Hove singularity in the topology critical point of bilayer hyperbolic metamaterials (Conference Presentation)", Proc. SPIE 10722, Plasmonics: Design, Materials, Fabrication, Characterization, and Applications XVI, 107221A (17 September 2018); https://doi.org/10.1117/12.2321048
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Vitally Pustovit, David Zelmon, Kurt Eyink, Augustine Urbas, "A Van Hove singularity in the topology critical point of bilayer hyperbolic metamaterials (Conference Presentation)," Proc. SPIE 10722, Plasmonics: Design, Materials, Fabrication, Characterization, and Applications XVI, 107221A (17 September 2018); https://doi.org/10.1117/12.2321048