论文标题
亚对称拓扑状态
Sub-symmetry protected topological states
论文作者
论文摘要
受对称保护的拓扑阶段（SPT）的标志是受拓扑保护的边界状态，它不受尊重保护对称性的扰动。人们普遍认为，任何破坏SPT阶段的扰动都会摧毁边界状态。但是，通过引入和探索对扰动的较弱的亚对称性（子对称性）的要求，我们发现边界国家保护的性质实际上更为复杂。我们证明，即使使用原型的su-schrieffer-heeger（SSH）和呼吸kagome晶格（BKL）模型仅受到边界状态的保护，即使尽管总体拓扑不变性和SPT相位被子扰动扰动破坏。通过在光子晶格中采用明智控制的对称性破坏，我们在实验中证明了对拓扑状态的这种亚质量保护。此外，我们在BKLS中引入了远程跳跃对称性，该对称性解决了他们角落状态的拓扑性质的辩论。我们的结果适用于光子学以外的其他系统，预示了在不同物理环境中没有完整对称性的情况下，探索SPT阶段有趣的特性的可能性。
A hallmark of symmetry-protected topological phases (SPTs) are topologically protected boundary states, which are immune to perturbations that respect the protecting symmetry. It is commonly believed that any perturbation that destroys an SPT phase simultaneously destroys the boundary states. However, by introducing and exploring a weaker sub-symmetry (SubSy) requirement on perturbations, we find that the nature of boundary state protection is in fact more complex. We demonstrate that the boundary states are protected by only the SubSy using prototypical Su-Schrieffer-Heeger (SSH) and breathing Kagome lattice (BKL) models, even though the overall topological invariant and the SPT phase are destroyed by SubSy preserving perturbations. By employing judiciously controlled symmetry breaking in photonic lattices, we experimentally demonstrate such SubSy protection of topological states. Furthermore, we introduce a long-range hopping symmetry in BKLs, which resolves a debate on the topological nature of their corner states. Our results apply to other systems beyond photonics, heralding the possibility of exploring the intriguing properties of SPT phases in the absence of full symmetry in different physical contexts.
