Moving Morphable Components-based inverse design formulation for quantum valley/spin hall insulators

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.