Supplying topologically protected wave propagation immune to backscattering, design of novel materials analogous to topological insulators is of great interest in different physical systems. Most of the related studies relies on designer’s intuition or pre-knowledge, and is achieved through a trail-and-error process. In order to present a unified and rational design approach applicable to quantum valley/spin Hall insulators (QVHIs/QSHIs), a mathematical programming is proposed by combining the band theory and the Moving Morphable Components (MMC) topology optimization method. The key idea is to directly obtain a pair of unit cells with both reverse-ordered gapped Dirac cones and maximized working bandwidth through the optimization process. This design paradigm can be generalized for the systematic design of optimized 2D/3D topological insulators among different physical systems.

提供不受反向散射影响的受拓扑保护的波传播，类似于拓扑绝缘体的新型材料的设计在不同的物理系统中引起了极大的兴趣。大多数相关研究依赖于设计师的直觉或预知，并且是通过跟踪和错误过程来实现的。为了提出一种适用于量子谷/自旋霍尔绝缘子（QVHIs / QSHIs）的统一合理的设计方法，通过结合能带理论和可移动变形组件（MMC）拓扑优化方法，提出了一种数学编程方法。关键思想是通过优化过程直接获得具有反向顺序的带间隙的狄拉克锥和最大工作带宽的一对晶胞。