Semi-Dirac points in phononic crystals

Handle URI:
http://hdl.handle.net/10754/564874
Title:
Semi-Dirac points in phononic crystals
Authors:
Zhang, Xiujuan ( 0000-0002-2375-3449 ) ; Wu, Ying ( 0000-0002-7919-1107 )
Abstract:
A semi-Dirac cone refers to a peculiar type of dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. It was originally discovered in electron systems, in which the associated quasi-particles are massless along one direction, like those in graphene, but effective-mass-like along the other. It was reported that a semi-Dirac point is associated with the topological phase transition between a semi-metallic phase and a band insulator. Very recently, the classical analogy of a semi-Dirac cone has been reported in an electromagnetic system. Here, we demonstrate that, by accidental degeneracy, two-dimensional phononic crystals consisting of square arrays of elliptical cylinders embedded in water are also able to produce the particular dispersion relation of a semi-Dirac cone in the center of the Brillouin zone. A perturbation method is used to evaluate the linear slope and to affirm that the dispersion relation is a semi-Dirac type. If the scatterers are made of rubber, in which the acoustic wave velocity is lower than that in water, the semi-Dirac dispersion can be characterized by an effective medium theory. The effective medium parameters link the semi-Dirac point to a topological transition in the iso-frequency surface of the phononic crystal, in which an open hyperbola is changed into a closed ellipse. This topological transition results in drastic change in wave manipulation. On the other hand, the theory also reveals that the phononic crystal is a double-zero-index material along the x-direction and photonic-band-edge material along the perpendicular direction (y-direction). If the scatterers are made of steel, in which the acoustic wave velocity is higher than that in water, the effective medium description fails, even though the semi-Dirac dispersion relation looks similar to that in the previous case. Therefore different wave transport behavior is expected. The semi-Dirac points in phononic crystals described in this work would offer new ways to manipulate acoustic waves with simple periodic structures. Copyright © 2014 by ASME.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Waves in Complex Media Research Group
Publisher:
ASME International
Journal:
Volume 13: Vibration, Acoustics and Wave Propagation
Conference/Event name:
ASME 2014 International Mechanical Engineering Congress and Exposition, IMECE 2014
Issue Date:
1-Jan-2014
DOI:
10.1115/IMECE2014-37421
Type:
Conference Paper
ISBN:
9780791849620
Appears in Collections:
Conference Papers; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorZhang, Xiujuanen
dc.contributor.authorWu, Yingen
dc.date.accessioned2015-08-04T07:23:46Zen
dc.date.available2015-08-04T07:23:46Zen
dc.date.issued2014-01-01en
dc.identifier.isbn9780791849620en
dc.identifier.doi10.1115/IMECE2014-37421en
dc.identifier.urihttp://hdl.handle.net/10754/564874en
dc.description.abstractA semi-Dirac cone refers to a peculiar type of dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. It was originally discovered in electron systems, in which the associated quasi-particles are massless along one direction, like those in graphene, but effective-mass-like along the other. It was reported that a semi-Dirac point is associated with the topological phase transition between a semi-metallic phase and a band insulator. Very recently, the classical analogy of a semi-Dirac cone has been reported in an electromagnetic system. Here, we demonstrate that, by accidental degeneracy, two-dimensional phononic crystals consisting of square arrays of elliptical cylinders embedded in water are also able to produce the particular dispersion relation of a semi-Dirac cone in the center of the Brillouin zone. A perturbation method is used to evaluate the linear slope and to affirm that the dispersion relation is a semi-Dirac type. If the scatterers are made of rubber, in which the acoustic wave velocity is lower than that in water, the semi-Dirac dispersion can be characterized by an effective medium theory. The effective medium parameters link the semi-Dirac point to a topological transition in the iso-frequency surface of the phononic crystal, in which an open hyperbola is changed into a closed ellipse. This topological transition results in drastic change in wave manipulation. On the other hand, the theory also reveals that the phononic crystal is a double-zero-index material along the x-direction and photonic-band-edge material along the perpendicular direction (y-direction). If the scatterers are made of steel, in which the acoustic wave velocity is higher than that in water, the effective medium description fails, even though the semi-Dirac dispersion relation looks similar to that in the previous case. Therefore different wave transport behavior is expected. The semi-Dirac points in phononic crystals described in this work would offer new ways to manipulate acoustic waves with simple periodic structures. Copyright © 2014 by ASME.en
dc.publisherASME Internationalen
dc.titleSemi-Dirac points in phononic crystalsen
dc.typeConference Paperen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentWaves in Complex Media Research Groupen
dc.identifier.journalVolume 13: Vibration, Acoustics and Wave Propagationen
dc.conference.date14 November 2014 through 20 November 2014en
dc.conference.nameASME 2014 International Mechanical Engineering Congress and Exposition, IMECE 2014en
kaust.authorWu, Yingen
kaust.authorZhang, Xiujuanen
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