Dirac Cones at k=0 in Phononic Crystals

Abstract

We show that two-dimensional phononic crystals exhibit Dirac cone dispersion at k=0 by exploiting dipole and quadrupole accidental degeneracy. While the equi-frequency surface of Dirac cone modes is isotropic, such systems exhibit "super-anisotropy", meaning that only transverse waves are allowed along certain directions while only longitudinal waves are allowed along some other directions. Only one mode, not two, is allowed near the Dirac point, and only two effective parameters, not four, are needed to describe the dispersion. Effective medium theory finds that the phononic crystals have effectively zero mass density and zero 1/C44 at the Dirac point. Numerical simulations are used to demonstrate the unusual elastic wave properties near the Dirac point frequency.

This paper has been withdrawn by the author due to publishing in journal

References in corpus (13)

• Analogs of quantum Hall effect edge states in photonic crystals
• Epsilon-Near-Zero (ENZ) Metamaterials and Electromagnetic Sources: Tailoring the Radiation Phase Pattern
• Broadband Acoustic Cloak for Ultrasound Waves
• Reverse Doppler Effect of Sound
• Acoustic cloaking theory
• Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal
• Super-reflection and Cloaking Based on Zero Index Metamaterial
• Extremal transmission at the Dirac point of a photonic band structure
• Photonic analog of graphene model and its extension -- Dirac cone, symmetry, and edge states --
• Extremal transmission and beating effect of acoustic wave in two-dimensional sonic crystal
• Effective theory of quadratic degeneracies
• Dirac Spectra and Edge States in Honeycomb Plasmonic Lattices
• Dispersion Relations and Their Symmetry Properties for Electromagnetic and Elastic Metamaterials in Two Dimensions

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