Inverse design of quantum spin hall-based phononic topological insulators

S. S. Nanthakumar, Xiaoying Zhuang, Harold S. Park, Chuong Nguyen, Yanyu Chen, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

64 Citations (Scopus)


We propose a computational methodology to perform inverse design of quantum spin hall effect (QSHE)-based phononic topological insulators. We first obtain two-fold degeneracy, or a Dirac cone, in the band structure using a level set-based topology optimization approach. Subsequently, four-fold degeneracy, or a double Dirac cone, is obtained by using zone folding, after which breaking of translational symmetry, which mimics the effect of strong spin-orbit coupling and which breaks the four-fold degeneracy resulting in a bandgap, is applied. We use the approach to perform inverse design of hexagonal unit cells of C 6 and C 3 symmetry. The numerical examples show that a topological domain wall with two variations of the designed metamaterials exhibit topologically protected interfacial wave propagation, and also demonstrate that larger topologically-protected bandgaps may be obtained with unit cells based on C 3 symmetry.

Original languageEnglish
Pages (from-to)550-571
Number of pages22
JournalJournal of the Mechanics and Physics of Solids
Publication statusPublished - 2019 Apr

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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