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Sci Rep. 2014 Apr 9;4:4613. doi: s10.1038/srep04613.

Accidental degeneracy of double Dirac cones in a phononic crystal.

Author information

  • 1National Laboratory of Solid State Microstructures & Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, People's Republic of China.
  • 2Division of Mathematical and Computer Sciences and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia.


Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of the Brillouin zone in a two-dimensional honeycomb lattice phononic crystal, which is a result of accidental degeneracy of two double-degenerate states. In the vicinity of the quadruple-degenerate state, the dispersion relation is linear. Such quadruple degeneracy is analyzed by rigorous representation theory of groups. Using k·p method, a reduced Hamiltonian is obtained to describe the linear Dirac dispersion relations of this quadruple-degenerate state, which is well consistent with the simulation results. Near such accidental degeneracy, we observe some unique properties in wave propagating, such as defect-insensitive propagating character and the Talbot effect.

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