非厄米平带的分类
Classification of Non-Hermitian Flat Bands
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中文总结 AI 辅助
本文提出基于双正交投影子的非厄米平带分类，揭示其四类特性，发现投影子连续性可锁定陈数，NH-E类陈数不匹配能增强共振跨轨道转移，确立投影子正则性为核心组织原则。
中文摘要 AI 辅助
精确平带为关联与拓扑现象提供了通用的研究场景，其特性不仅由色散关系控制，还受布洛赫投影子的结构影响。本文建立了基于投影子的非厄米平带分类方法。与厄米平带不同，非厄米性引入了双正交投影子，其左右配对允许出现独特的范数极点奇点。我们确定了四类：解析的NH-A类、连续但非解析的NH-C类、有界但不连续的NH-D类以及极点奇异的NH-E类。研究表明，双正交投影子的连续性保持了右、左及双正交陈数的锁定关系，即$C_R=C_L=C_{\rm bi}$，从而实现非厄米临界拓扑平带。一旦连续性丧失，这种锁定关系可能被打破；特别地，NH-E类中会出现$C_R\neq C_L$的不匹配情况。最后，我们证明这种陈数不匹配可导致共振跨轨道转移的异常增强。本研究确立了双正交投影子正则性作为关联非厄米平带中紧致局域态、拓扑与驱动响应的组织原则。
英文摘要
Exact flat bands provide a versatile setting for correlated and topological phenomena, yet their properties are controlled not only by their dispersion but also by the structure of their Bloch projectors. Here, we establish a projector-based classification of non-Hermitian flat bands. In contrast to Hermitian flat bands, non-Hermiticity introduces a biorthogonal projector whose left-right pairing permits a distinct norm-pole singularity. We identify four classes: analytic NH-A, continuous but nonanalytic NH-C, bounded but discontinuous NH-D, and pole-singular NH-E. We show that continuity of the biorthogonal projector preserves the locking of the right, left, and biorthogonal Chern numbers, $C_R=C_L=C_{\rm bi}$, thereby realizing non-Hermitian critical topological flat bands. Once continuity is lost, this locking can break down; in particular, a mismatch $C_R\neq C_L$ can occur in the NH-E class. Finally, we show that this Chern number mismatch ensures to produce an anomalous enhancement of resonant cross-orbital transfer. Our results establish biorthogonal projector regularity as the organizing principle linking compact localized states, topology, and driven response in non-Hermitian flat bands.
