发表机构
Emory University（埃默里大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究构建了一种无试探态、规范不变的激子空间定位器，可同时最大程度局域激子组分电子和空穴坐标，适用于通用多带情况，在特定双层模型中揭示了相关对称性对激子瓦尼尔函数偶极矩的约束。
AI 中文摘要
激子的内部电子-空穴结构会影响光学和电场响应。激子瓦尼尔函数近期为激子能带提供了实空间的局域表示。由于激子是复合准粒子，这些瓦尼尔函数可通过其质心位置和内部电子-空穴偶极矩来表征。在实空间中分辨该内部结构需要同时确定组分电子和空穴的坐标。然而，投影后的电子和空穴位置算符通常不对易，因此这些位置无法同时对角化：它们的不对易性排除了共同本征基，并对联合展宽施加了与状态相关的下限。现有方法仅定位单个平均坐标或特定组分坐标，通常无法构建能最大程度同时局域两个组分坐标的共同激子瓦尼尔基。在此，我们构建了一种“激子空间定位器”：单个厄米算符，其将组分位置算符嵌入克利福德代数结构并返回激子瓦尼尔函数，该函数在电子和空穴坐标上同时达到最大局域化。我们的公式无试探态、规范不变，适用于通用多带情况。在具有孤立激子能带组的相互作用双层模型中，我们表明反射和时间反演对称性，或本文详述的其他非简单空间群对称性，强制逐点无迹但非零的量子几何偶极矩矩阵，其表现为具有相等且相反内部电子-空穴偶极矩的对称相关激子瓦尼尔函数对。
英文摘要
Excitons are composite quasiparticles: beyond a center-of-mass position, each carries an internal electron-hole dipole governing its coupling to electric fields and other excitons. Exciton Wannier functions locally represent exciton bands, but resolving this dipole requires localizing the electron and hole simultaneously. We show that, in one dimension, the projected electron and hole position operators fail to commute when the covariant derivative of the quantum geometric dipole (QGD) matrix (the difference between the hole and electron non-Abelian Berry connections) is nonzero. This precludes a common eigenbasis and bounds the joint electron-hole spread from below. For one band, the internal dipole is gauge invariant and center-of-mass methods suffice; for multiple bands, no existing construction yields a gauge minimizing both position uncertainties. We introduce an ``exciton spatial localizer,'' a Hermitian operator embedding both projected positions in a Clifford-algebra structure. Its spectral minima locate the exciton's center-of-mass and dipole coordinates, while its eigenvectors yield exciton Wannier functions jointly localized in electron and hole coordinates without gauge fixing, an ansatz, or iterative optimization. In an interacting bilayer model, combined reflection--time-reversal symmetry or a nonsymmorphic particle--hole symmetry forces the QGD matrix to be traceless at every momentum while allowing it to remain nonzero. A two-band exciton subspace with zero net internal dipole then decomposes into a symmetry-related pair of exciton Wannier functions with opposite center-of-mass positions and internal dipoles. Adding the interlayer dipole as a Clifford component further separates intralayer and interlayer exciton Wannier functions in a six-band subspace.
