Efficient Design of Helical Higher-Order Topological Insulators in 3D Elastic Medium

Abstract

Topological materials (TMs) are well-known for their topological protected properties. Phononic system has the advantage of direct observation and engineering of topological phenomena on the macroscopic scale. For the inverse design of 3D TMs in continuum medium, however, it would be extremely difficult to classify the topological properties, tackle the computational complexity, and search solutions in an infinite parameter space. This work proposed a systematic design framework for the 3D mechanical higher-order topological insulators (HOTIs) by combining the symmetry indicators (SI) method and the moving morphable components (MMC) method. The 3D unit cells are described by the MMC method with only tens of design variables. By evaluating the inherent singularity properties in the 3D mechanical system, the classic formulas of topological invariants are modified accordingly for elastic waves. Then a mathematical formulation is proposed for designing the helical multipole topological insulators (MTIs) featured corner states and helical energy fluxes, by constraining the corresponding topological invariants and maximizing the width of band gap. Mechanical helical HOTIs with different symmetries are obtained by this method and verified by full wave simulations. This design paradigm can be further extended to design 3D TMs among different symmetry classes and space groups, and different physical systems.

References in corpus (9)

• Topological Insulators with Inversion Symmetry
• Topological Photonics
• Scheme to Achieve Silicon Topological Photonics
• Topology optimization based on moving deformable components: A new computational framework
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• A multi-material level set-based topology optimization of flexoelectric composites
• An efficient and easy-to-extend Matlab code of the Moving Morphable Component (MMC) method for three-dimensional topology optimization
• Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem
• Double Dirac Cones and Topologically Non-Trivial Phonons for Continuous, Square Symmetric (C${}_{4v}$ and C${}_{2v}$) Unit Cells