无序弹性量子自旋霍尔系统中的拓扑相变
Topological phase transition in disordered elastic quantum spin Hall system
AI总结：
研究二维力学系统中无序对拓扑态的影响，提出基于弹簧-质量模型的量子自旋霍尔绝缘体，用自旋Bott指数表征并验证无序诱导的拓扑相变，设计声子晶体证实边界拓扑保护态。
摘要：
我们研究了二维（2D）力学系统中无序对拓扑非平凡态的影响。首先，我们基于面外弹簧-质量模型提出了一种量子自旋霍尔（QSH）绝缘体，并解析地研究了在拓扑平凡和非平凡系统中无序与拓扑之间的相互作用。我们采用自旋 Bott 指数来表征无序力学系统中的拓扑性质。通过追踪自旋 Bott 指数随无序增强的演化，我们定量地证明了从拓扑非平凡的 QSH 绝缘体到平凡绝缘体的无序诱导转变。随后，我们通过离散晶格中的瞬态分析验证了拓扑相变。最后，我们基于离散弹簧-质量模型设计了一种声子晶体，并在连续系统中数值验证了平凡绝缘体与无序拓扑 QSH 绝缘体边界上的拓扑保护态。这项工作在理解二维拓扑经典系统中无序的作用方面向前迈进了一步。
英文摘要：
We investigate the effect of disorder on topologically nontrivial states in a two dimension (2D) mechanical system. We first propose a quantum spin Hall (QSH) insulator based on an out-of-plane spring-mass model and analytically study the interplay between the disorder and topology in both topologically trivial and nontrivial systems. We adopt the spin Bott index to characterize the topological property in disordered mechanical systems. By tracking the evolution of the spin Bott index with the increase of disorders, we quantitatively demonstrate the disorder induced transition from a topologically nontrivial QSH insulator to a trivial insulator. We then validate the topological phase transition through transient analysis in discrete lattices. Finally, we design a phononic crystal based on the discrete spring-mass model and numerically verify the topologically protected states along the boundary between the trivial insulator and disordered topological QSH insulator in a continuous system. This work puts a step forward in understanding the role of disorder in a 2D topological classical system.
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