科赫分形几何中的手征对称性破缺与简并性
Chiral-symmetry breaking and degeneracy in Koch fractal geometries
- Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
研究科赫曲线上的SSH模型，发现三角形几何打破手征对称性，局域干涉产生$E=-t$处的简并平带，其简并度受分形连接性调控，明确局域干涉与全局连接性对SSH链电子性质的互补作用。
中文摘要 AI 辅助
分形几何为调控量子干涉、拓扑与局域化提供了独特平台。我们研究构建于科赫曲线上的Su-Schrieffer-Heeger（SSH）模型，其中三角形几何结构引入额外的同子晶格跳跃，打破手征对称性并改变实空间局域标记所表征的常规拓扑行为。三角形单元内的相消干涉在$E=-t$处产生高度简并的平带能级。尽管该能级源于局域几何结构，但其简并度与谱权重受科赫曲线的自相似连接性调控。这种层级结构减少了独立平带态的数量，并将谱重组为复杂的能级分布。我们的结果揭示了局域三角形干涉与全局分形连接性在塑造几何修饰SSH链电子性质中的互补作用。
英文摘要
Fractal geometries provide a distinctive platform for controlling quantum interference, topology, and localization. We investigate the Su--Schrieffer--Heeger (SSH) model constructed on the Koch curve, where a triangular geometry enables additional same-sublattice hoppings that break chiral symmetry and modify the conventional topological behavior captured by a real-space local marker. Destructive interference within the triangular units produces a highly degenerate flat level at $E=-t$. Although this level originates from the local geometry, its degeneracy and spectral weight are controlled by the self-similar connectivity of the Koch curve. The hierarchy reduces the number of independent flat states and reorganizes the spectrum into an intricate distribution of energy levels. Our results reveal complementary roles for local triangular interference and global fractal connectivity in shaping the electronic properties of geometrically modified SSH chains.
