Topology optimization of quantum spin Hall effect-based second-order phononic topological insulator

Yafeng Chen, Jensen Li, Jie Zhu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

34 Citations (Scopus)


Second-order phononic topological insulators (SPTIs) featured with topological edge and corner states offer promising ways for steering elastic waves. However, existing SPTIs were mainly designed with trial-and-error procedures, limiting the achievable width of topological bandgaps for tightly confining edge and corner states. Here, we develop a topology optimization approach for designing quantum spin Hall effect-based SPTIs. By simultaneously maximizing the powers emitted by the artificially selected body forces via topology optimization, the dipolar and quadrupolar modes are excited at the desirable frequencies. As a result, topologically nontrivial and trivial phononic crystals (PCs) with a record-breaking size of the overlapped bandgap (36.14%) are created. Thereafter, SPTIs arranged by hexagon and rhombus unit cells extracted from the optimized PCs are successfully created, validating the effectiveness of the optimization results. Additionally, the spatial decay of corner states is quantitatively characterized based on the complex band theory. Our work bridges topology optimization with SPTIs and, meanwhile, enriches the mechanism of corner states.

Original languageEnglish
Article number108243
JournalMechanical Systems and Signal Processing
Publication statusPublished - 1 Feb 2022


  • High-order topological insulator
  • Phononic crystals
  • Quantum spin Hall effect
  • Topology optimization

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Civil and Structural Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Computer Science Applications


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