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 journalArticle

13 Citations (Scopus)

Abstract

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 C6 and C3 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 C3 symmetry.

Original languageEnglish
Pages (from-to)550-571
Number of pages22
JournalJournal of the Mechanics and Physics of Solids
Volume125
DOIs
Publication statusPublished - 2019 Apr 1

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Cones
Energy gap
Spin Hall effect
insulators
Quantum Hall effect
Domain walls
Metamaterials
cones
Shape optimization
symmetry
Band structure
Wave propagation
Orbits
cells
folding
domain wall
Hall effect
wave propagation
topology
methodology

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Inverse design of quantum spin hall-based phononic topological insulators. / Nanthakumar, S. S.; Zhuang, Xiaoying; Park, Harold S.; Nguyen, Chuong; Chen, Yanyu; Rabczuk, Timon.

In: Journal of the Mechanics and Physics of Solids, Vol. 125, 01.04.2019, p. 550-571.

Research output: Contribution to journalArticle

Nanthakumar, S. S. ; Zhuang, Xiaoying ; Park, Harold S. ; Nguyen, Chuong ; Chen, Yanyu ; Rabczuk, Timon. / Inverse design of quantum spin hall-based phononic topological insulators. In: Journal of the Mechanics and Physics of Solids. 2019 ; Vol. 125. pp. 550-571.
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