Customizing acoustic dirac cones and topological insulators in square lattices by topology optimization

Hao Wen Dong, Sheng Dong Zhao, Rui Zhu, Yue Sheng Wang, Li Cheng, Chuanzeng Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

25 Citations (Scopus)


Dirac point, the cornerstone of topological insulators, has been attracting ever-increasing attention due to its extraordinary properties. In this paper, a bottom-up topology optimization approach is established to systematically design the acoustic Dirac cones with customized double, triple and quadruple degeneracies at different wavelength scales. Using the proposed methodology, novel square-symmetric, chiral and orthogonal-symmetric sonic crystals (SCs) are constructed in a square lattice with tailored Dirac cones. The proposed design approach offers a unified framework to tailor SCs with exotic functionalities which are being widely researched in acoustic metamaterial community. As illustrative examples, zero-index acoustic cloaking and Talbot effect near the Dirac points of the optimized SCs are demonstrated numerically. Moreover, a novel acoustic pseudo-spin topological insulator is obtained, which entails a robust zigzag wave propagation and broadband, unidirectional, and topologically protected transport with a record-breaking relative bandwidth of 30.51%. The proposed design methodology shows promise and opens new horizons for customizing topological acoustics and conceiving high-efficiency wave devices.

Original languageEnglish
Article number115687
JournalJournal of Sound and Vibration
Publication statusPublished - 17 Feb 2021


  • Degeneracy
  • Dirac cone
  • Quantum spin-hall effect
  • Sonic crystals
  • Topological insulator
  • Topology optimization

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering


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