发表机构
Institute of Theoretical Physics, Utrecht University（乌得勒支大学理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文发现能带拓扑可强制最低激子包络波函数出现动量空间零点，通过三带模型和Bethe-Salpeter方程求解验证，并分类了低维跃迁丛的拓扑激子节点结构。
AI 中文摘要
最低能量的激子通常预期具有无节点的$1s$型包络波函数。我们表明，能带拓扑可以阻碍这一预期。激子包络波函数是价带-导带跃迁丛的一个截面，其拓扑可以强制动量空间中的零点，这些零点的宇称或带符号的总指标由相应的特征类固定。我们在一个最小的$PT$对称三带模型中举例说明了这一行为，该模型具有由欧拉数$\nu^e=2$表征的秩二跃迁丛。通过直接求解具有接触和Rytova-Keldysh相互作用的Bethe-Salpeter方程，我们发现最低激子包含两个零点，每个指标为$+1$，并且其束缚强度弱于拓扑平凡的对应激子。我们进一步对维度$d \leq 3$中实数和复数跃迁丛的拓扑强制激子节点结构进行了分类。我们的结果确立了跃迁丛拓扑对激子波函数和光谱的直接约束。
英文摘要
Lowest-energy excitons are usually expected to have nodeless $1s$-like envelope wavefunctions. We show that band topology can obstruct this expectation. The exciton envelope wavefunction is a section of the valence-conduction transition bundle, whose topology can enforce momentum-space zeros, with their parity or signed total index fixed by the corresponding characteristic class. We exemplify this behavior in a minimal $PT$-symmetric three-band model with a rank-two transition bundle characterized by Euler number $ν^e=2$. By directly solving the Bethe-Salpeter equation with both contact and Rytova-Keldysh interactions, we find that the lowest exciton contains two zeros, each with index $+1$, and is less strongly bound than its topologically trivial counterpart. We further classify topology-enforced exciton nodal structures for real and complex transition bundles in dimensions $d \leq 3$. Our results establish the topology of the transition bundle as a direct constraint on exciton wavefunctions and spectra.
Comments10 pages 4, figures
