发表机构
International Center for Quantum Materials, School of Physics, Peking University; Beijing Key Laboratory of Quantum Devices; Collaborative Innovation Center of Quantum Matter（北京大学物理学院量子材料国际中心; 北京量子器件重点实验室; 量子物质协同创新中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出统一光学框架，通过张量Ioffe-Larkin响应测量拓扑莫特绝缘体中自旋子的量子几何，实现陈数与量子度量谱的重建。
AI 中文摘要
受近期电子能带中量子几何研究兴趣的启发，我们考虑一个二维拓扑莫特绝缘体，即手性自旋液体，其自旋子能带展现出非平凡的能带拓扑和量子几何。带隙电荷扇区的虚极化通过涌现的U(1)规范场将电磁驱动传递给电荷中性的自旋子，产生张量Ioffe-Larkin响应，并实现两种互补的光学测量协议。在离壳（低频）区域，物理纵向电导率与霍尔电导率的自校准比值可给出自旋子陈数，而无需电荷响应的微观知识。在壳（共振）区域，将逆Ioffe-Larkin响应与Kramers-Kronig关系相结合，可重建量子度量和贝里曲率谱密度。我们的方法直接适用于莫尔系统中的三角晶格Hofstadter-Hubbard模型，并可通过适当修改很好地适配其他三角晶格反铁磁体，如Nb$_3$Br$_8$。我们建立了一个统一框架，用于定量探测拓扑莫特体系中分数化准粒子的量子几何。
英文摘要
Inspired by recent interests in quantum geometry in electronic bands, we consider a two-dimensional topological Mott insulator, i.e. chiral spin liquid, whose spinon bands develop nontrivial band topological and quantum geometry. The virtual polarization of the gapped charge sector transfers the electromagnetic drive to the charge-neutral spinons through the emergent U(1) gauge field, producing a tensor Ioffe-Larkin response and enabling two complementary optical protocols for measurements. In the off-shell (low-frequency) regime, a self-calibrated ratio of the physical longitudinal and Hall conductivities yields the spinon Chern number without the microscopic knowledge of the charge response. In the on-shell (resonant) regime, combining the inverse Ioffe-Larkin response with the Kramers-Kronig relation enables reconstruction of the quantum-metric and Berry-curvature spectral densities. Our approach directly applies to the triangular lattice Hofstadter-Hubbard model in Moiré systems, can be well adapted to other triangular lattice antiferromagnets such as Nb$_3$Br$_8$ with appropriate modifications. We establish a unified framework for quantitatively probing the quantum geometry of fractionalized quasiparticles in topological Mott regime.
