Lattice materials with topological states optimized on demand

• 成果类型: Article
• 署名作者: Azizi, Pegah; Kundu, Rahuldev; Li, Weichen; Sun, Kai; Zhang, Xiaojia Shelly; Gonella, Stefano
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; University of Illinois System; University of Illinois Urbana-Champaign; University of Michigan System; University of Michigan
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-12874
• DOI: 10.1073/pnas.2506787122
• 发表日期: 2025-08-12
• 关键词: bilbao crystallographic server; DESIGN; REPRESENTATIONS; metamaterials; filters

摘要

Topological states of matter, first discovered in quantum systems, have opened new avenues for wave manipulation beyond the quantum realm. In elastic media, realizing these topological effects requires identifying lattices that support the corresponding topological bands. However, among the vast number of theoretically predicted topological states, only a small fraction has been physically realized. To close this gap, we present a strategy capable of systematically and efficiently discovering metamaterials with desired topological state. Our approach builds on topological quantum chemistry, which systematically classifies topological states by analyzing symmetry properties at selected wavevectors. Because this method condenses the topological character into mathematical information at a small set of wavevectors, it encodes a clear and computationally efficient objective for topology optimization algorithms. We demonstrate that, for certain lattice symmetries, this classification can be further reduced to intuitive morphological features of the phonon band structure. By incorporating these band morphology constraints into topology optimization algorithms and further fabricating obtained designs, we enable the automated discovery and physical realization of metamaterials with targeted topological properties. This methodology establishes a paradigm for engineering topological elastic lattices on demand, addressing the bottleneck in material realization and paving the way for a comprehensive database of topological metamaterial configurations.