发表机构
Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México（墨西哥国立自治大学理学院物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出将谐波振动系统映射为有效紧束缚哈密顿量的框架，验证了角弯链中的模式转换，并揭示锯齿形链中几何畴壁可恢复隙内局域态，实现共振透射。
AI 中文摘要
我们提出一个框架，将谐波振动系统映射到有效的多轨道紧束缚哈密顿量上，从而在声子自由度与基于图的晶格模型之间建立直接对应关系。在此映射中，每个质量的笛卡尔位移分量成为内部轨道，而弹性相互作用则生成由系统几何决定的有效在位能和跳跃振幅。这种表示使得原本为电子输运开发的数值和概念工具能够应用于声子体系的研究。该方法首先应用于包含角弯的单原子链。对于这一基准系统，我们推导了偏振分辨的透射和反射概率的解析表达式，并与在映射后的紧束缚表示中采用递归散射矩阵法进行的计算进行了比较。获得了极好的一致性，验证了该映射的有效性，并展示了其描述几何诱导模式转换和倏逝态影响的能力。随后我们研究了锯齿形链，其中交替的键取向生成类似于苏-施里弗-黑格（SSH）模型的有效二聚化哈密顿量。尽管均匀锯齿形链会形成谱隙，但未观察到局域边缘态。我们表明，由声子映射产生的修正边界参数抑制了理想SSH图像所预期的边缘态形成。引入几何畴壁可在隙内恢复局域畴壁态，这些态在原本绝缘的频率窗口内产生共振透射通道。共振能量对系统尺寸变化保持稳健，相应的透射率趋近于1。
英文摘要
We present a framework that maps harmonic vibrational systems onto effective multi-orbital tight-binding Hamiltonians, establishing a direct correspondence between phononic degrees of freedom and graph-based lattice models. Within this mapping, the Cartesian displacement components of each mass become internal orbitals, while elastic interactions generate effective onsite energies and hopping amplitudes determined by the geometry of the system. This representation enables the application of numerical and conceptual tools originally developed for electronic transport to the study of phononic systems. The method is first applied to a monoatomic chain containing an angular bend. For this benchmark system, analytical expressions for the polarization-resolved transmission and reflection probabilities are derived and compared against calculations performed using a recursive scattering-matrix method within the mapped tight-binding representation. Excellent agreement is obtained, validating the mapping and demonstrating its ability to describe geometry-induced mode conversion and the influence of evanescent states. We then investigate zigzag chains, where alternating bond orientations generate effective dimerized Hamiltonians reminiscent of the Su--Schrieffer--Heeger (SSH) model. Although the uniform zigzag chain develops a spectral gap, no localized edge states are observed. We show that modified boundary parameters generated by the phononic mapping suppress the edge-state formation expected from the ideal SSH picture. Introducing a geometric domain wall restores localized domain-wall states inside the gap, which give rise to resonant transmission channels across an otherwise insulating frequency window. The resonance energies remain robust against system-size variations and the corresponding transmission approaches unity.
Comments23 pages, 8 figures
