Rotational modes in a phononic crystal with fermion-like behavior

Research output: Contribution to journalArticle

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Abstract

The calculated band structure of a two-dimensional phononic crystal composed of stiff polymer inclusions in a soft elastomer matrix is shown to support rotational modes. Numerical calculations of the displacement vector field demonstrate the existence of modes whereby the inclusions and the matrix regions between inclusions exhibit out of phase rotations but also in phase rotations. The observation of the in-phase rotational mode at low frequency is made possible by the very low transverse speed of sound of the elastomer matrix. A one-dimensional block-spring model is used to provide a physical interpretation of the rotational modes and of the origin of the rotational modes in the band structure. This model is analyzed within Dirac formalism. Solutions of the Dirac-like wave equation possess a spinor part and a spatio-temporal part. The spinor part of the wave function results from a coupling between the senses (positive or negative) of propagation of the wave. The wave-number dependent spinor-part of the wave function for two superposed waves can impose constraints on the integral of the spatio-temporal part that are reflected in a fermion-like lifting of degeneracy in the phonon band structure associated with in-phase rotations.

Original languageEnglish (US)
Article number163510
JournalJournal of Applied Physics
Volume115
Issue number16
DOIs
StatePublished - Apr 28 2014

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fermions
crystals
inclusions
elastomers
matrices
wave functions
wave equations
formalism
low frequencies
propagation
acoustics
polymers

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Rotational modes in a phononic crystal with fermion-like behavior. / Deymier, Pierre A; Runge, Keith A; Swinteck, N.; Muralidharan, Krishna.

In: Journal of Applied Physics, Vol. 115, No. 16, 163510, 28.04.2014.

Research output: Contribution to journalArticle

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