准晶的动量分辨电子结构：全带谱与陈数
Momentum-Resolved Electronic Structure for Quasicrystals: Full-Band Spectra and Chern Number
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中文总结 AI 辅助
针对准晶缺乏平移对称性导致全带动量分辨电子结构难以计算的问题，提出结合傅里叶模散射通道哈密顿量与赝布里渊区层级的倒空间紧束缚框架，在彭罗斯和阿曼-比恩克模型中揭示全带准带、赝能隙机制及陈数平台等拓扑性质。
中文摘要 AI 辅助
准晶缺乏平移对称性，而平移对称性是布洛赫分解和布里渊区积分的基础，这使得全带动量分辨电子结构的表述和计算变得困难。我们为一大类准晶开发了一个系统收敛的倒空间紧束缚框架。该方法结合了两个系统可细化的组成部分：一个傅里叶模散射通道哈密顿量，用于在每个物理动量处产生局域谱和流-流关联量；以及一个扩展的赝布里渊区层级，通过精确的局域到全局关系将所得的局域量转换为体热力学可观测量。将该框架应用于彭罗斯和阿曼-比恩克模型，揭示了全带动量分辨准带和赝能隙形成的多通道机制，这两者都超出了低能有效模型的范围。该框架还进一步解析了塞曼驱动的能隙闭合与重新打开、量子化陈数平台以及体谱和拓扑可观测量对相位子的不变性。该框架为准晶的全带谱和拓扑性质提供了一条统一的倒空间路径。
英文摘要
Quasicrystals lack the translational symmetry that underlies Bloch decomposition and Brillouin-zone integration, making full-band momentum-resolved electronic structure difficult to formulate and compute. We develop a systematically convergent reciprocal-space tight-binding framework for a broad class of quasicrystals. The method combines two systematically refinable components: a Fourier-module scattering-channel Hamiltonian that yields local spectral and current-current correlation quantities at each physical momentum, and an expanding hierarchy of pseudo-Brillouin zones that converts the resulting local quantities into bulk thermodynamic observables through an exact local-to-global relation. Applied to the Penrose and Ammann-Beenker models, the framework uncovers full-band momentum-resolved quasibands and a multichannel mechanism for pseudogap formation, both beyond the scope of low-energy effective models. It further resolves Zeeman-driven gap closings and reopenings, quantized Chern plateaus, and the phason invariance of bulk spectral and topological observables. This framework provides a unified reciprocal-space route to full-band spectral and topological properties of quasicrystals.
发表机构
- School of Mathematical Sciences, Beijing Normal University（北京师范大学数学科学学院）
- Faculty of Arts and Sciences, Beijing Normal University（北京师范大学文理学院）
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