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

TL;DR

This paper introduces a systematic framework combining symmetry indicators and moving morphable components to efficiently design 3D higher-order topological insulators in elastic media, enabling targeted control of topological properties.

Contribution

It develops a novel design method for 3D mechanical HOTIs using symmetry indicators and MMC, simplifying the complex inverse design process in continuum media.

Findings

Successfully designed 3D mechanical HOTIs with various symmetries

Verified topological corner states and helical energy fluxes via simulations

Maximized band gap width through constrained topological invariants

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.