AI 中文总结
研究在缩放耦合模型和霍夫施塔特模型中实现位错诱导捕获态，通过将缩放耦合模型捕获模式视为连续体中更高局域态，以及用Householder三对角化处理霍夫施塔特模型，为设计高度局域模式提供实用途径，推动弹性波系统拓扑物理发展。
AI 中文摘要
弹性拓扑位错为在内部缺陷处捕获弹性波能量提供了途径，而非仅局限于外部边界或角落。但存在两个实际限制：传统SSH二聚化的高度受限位错态通常需要大耦合对比度和相应增大的带隙，难以实现；一些含更丰富拓扑物理的哈密顿量包含复杂跳跃项等，增加实验样本几何复杂性。本文在弹性平台的缩放耦合模型和霍夫施塔特模型中展示了位错诱导的捕获态。在缩放耦合模型中，捕获模式被视为连续体中的更高局域态，无需增大带隙就能捕获增强模式；对于霍夫施塔特模型，用Householder三对角化将含复杂跳跃项的原始紧束缚哈密顿量映射为仅含正实值最近邻跳跃项的三对角矩阵，在弱跳跃位置截断保留拓扑现象并能从缩短的非周期链构建位错缺陷。结果为设计高度局域模式建立了实用途径，推动了弹性波系统的拓扑物理发展，为弹性功能器件带来更多可能。
英文摘要
Elastic topological dislocations provide a pathway for trapping elastic wave energy at internal defects, rather than being confined solely to external boundaries or corners, which are typically associated with topological insulators (TIs). However, two practical constraints persist. First, highly confined dislocation states based on conventional Su-Schrieffer-Heeger (SSH) dimerization usually require a large coupling contrast and a correspondingly enlarged bandgap, which may be challenging to realize. Second, some Hamiltonians with richer topological physics often contain complex hopping terms, synthetic gauge fields or nonlocal couplings, which substantially increase the geometric complexity of experimental samples. Here, dislocation-induced trapped states are demonstrated in both a scaled coupling (SC) model and a Hofstadter model (HM) within an elastic platform. In the SC model, the trapped mode is treated as a higher localized state in the continuum rather than an in-gap mode in the SSH model. Consequently, the SC-induced dislocation can trap an enhanced mode without the requirement of an enlarged bandgap. For the HM, Householder tridiagonalization is used to map the original tight-binding Hamiltonian with complex hopping terms onto a tridiagonal matrix with only positive-real-valued nearest-neighbour (NN) hopping terms. Truncation at a weak-hopping position preserves the topological phenomena and allows a dislocation defect to be constructed from the shortened aperiodic chain. The results establish a practical route for designing highly localized modes without relying solely on bandgap enlargement or complex couplings, which advance the topological physics of elastic wave systems and promise enhanced possibilities for elastic functional devices.
