Manipulating Möbius edge states in elastic wave phononic crystals

作者：Shengnan Liang, Jian-Lan Xie, Cheng He, Si‐Yuan Yu, Yan-Feng Chen · 发表于：Physical review. B./Physical review. B · 年份：2025 · DOI：10.1103/physrevb.111.184103 · 被引用次数：2 · 研究领域：Topological Materials and Phenomena、Metamaterials and Metasurfaces Applications、Nonlinear Photonic Systems

Employing the gauge representation of crystalline symmetries necessitates capturing their algebraic structure in a projective form. As such, the projectively represented space group (PRSG) offers a powerful framework for uncovering novel topological phases and enhancing our understanding of topological band theory. Meanwhile, the tunable ${\mathbb{Z}}_{2}$ gauge field inherent in artificial crystals underpins the practical implementation of PRSG. Indeed, the PRSG mechanism has fueled significant progress in discovering new topological phases within photonic and phononic crystals (PnCs). In this work, we incorporate projectively translational symmetry into elastic wave PnCs and demonstrate the resulting emergence of M\"obius edge states. Beyond exhibiting a ${\mathbb{Z}}_{2}$ topological phase that diverges from the conventional two-dimensional Su-Schrieffer-Heeger model, our system also offers controllability over M\"obius edge states: by simply adjusting the coupling tubes, the fourfold degeneracy at high-symmetry points can be shifted, accompanied by the concurrent displacement of the M\"obius edge states. These findings not only demonstrate the introduction of negative coupling in elastic wave PnCs but also leverage projectively translational symmetry---realized through such negative coupling---to both realize and precisely manipulate M\"obius edge states. Our results thus establish a fundamental platform for devising topological phases based on PRSG in elastic wave system...