Inverse design of quantum spin hall-based phononic topological insulators

authored by: Srivilliputtur Subbiah Nanthakumar, Xiaoying Zhuang, Harold S. Park, Thanh Chuong Nguyen, Yanyu Chen, Timon Rabczuk
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 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.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Tongji University
Dalian University of Technology
Boston University (BU)
University of Louisville
Ton Duc Thang University
King Saud University
Type: Article
Journal: Journal of the Mechanics and Physics of Solids
Volume: 125
Pages: 550-571
No. of pages: 22
ISSN: 0022-5096
Publication date: 04.2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Condensed Matter Physics, Mechanics of Materials, Mechanical Engineering
Electronic version(s): https://doi.org/10.1016/j.jmps.2019.01.009 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{980fe1071a524aca8b99eaa8197f994a,
title = "Inverse design of quantum spin hall-based phononic topological insulators",
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 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. ",
author = "Nanthakumar, {Srivilliputtur Subbiah} and Xiaoying Zhuang and Park, {Harold S.} and Nguyen, {Thanh Chuong} and Yanyu Chen and Timon Rabczuk",
note = "Funding information: HSP acknowledges the support of the Army Research Office , grant W911NF-18-1-0380 .",
year = "2019",
month = apr,
doi = "10.1016/j.jmps.2019.01.009",
language = "English",
volume = "125",
pages = "550--571",
journal = "Journal of the Mechanics and Physics of Solids",
issn = "0022-5096",
publisher = "Elsevier Ltd.",
}