# Semi-Dirac points in phononic crystals

- Handle URI:
- http://hdl.handle.net/10754/564874
- Title:
- Semi-Dirac points in phononic crystals
- Authors:
- 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:
- Publisher:
- Journal:
- 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 Field | Value | Language |
---|---|---|

dc.contributor.author | Zhang, Xiujuan | en |

dc.contributor.author | Wu, Ying | en |

dc.date.accessioned | 2015-08-04T07:23:46Z | en |

dc.date.available | 2015-08-04T07:23:46Z | en |

dc.date.issued | 2014-01-01 | en |

dc.identifier.isbn | 9780791849620 | en |

dc.identifier.doi | 10.1115/IMECE2014-37421 | en |

dc.identifier.uri | http://hdl.handle.net/10754/564874 | en |

dc.description.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. | en |

dc.publisher | ASME International | en |

dc.title | Semi-Dirac points in phononic crystals | en |

dc.type | Conference Paper | en |

dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | en |

dc.contributor.department | Applied Mathematics and Computational Science Program | en |

dc.contributor.department | Waves in Complex Media Research Group | en |

dc.identifier.journal | Volume 13: Vibration, Acoustics and Wave Propagation | en |

dc.conference.date | 14 November 2014 through 20 November 2014 | en |

dc.conference.name | ASME 2014 International Mechanical Engineering Congress and Exposition, IMECE 2014 | en |

kaust.author | Wu, Ying | en |

kaust.author | Zhang, Xiujuan | en |

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