AI 中文总结
研究基于克莱默斯-克朗尼格关系，推导并应用通用表达式关联低频准直流与高频光学霍尔响应，用于TRSB物质状态。通过参数图和实验数据验证，还据此预测铜酸盐超导体的反常霍尔效应值，鼓励探索，处理与量子几何相关工作有相似性。
AI 中文摘要
基于克莱默斯-克朗尼格关系，我们推导并应用了一个相当通用的表达式，该表达式将低频准直流霍尔电导率与渐近高频光学霍尔响应（及其在克尔和法拉第效应中的表现）联系起来，用于诸如铁磁体、破时间反演对称超导体以及处于磁场中的金属等破时间反演对称（TRSB）物质状态。参数图表明，对于尖锐回旋共振的平凡单模情况，该关系严格成立，对于铁磁体和TRSB超导体的理论模型则近似成立。我们还将其应用于各种铁磁系统的实验数据，也显示出合理的一致性。我们利用该关系从铜酸盐超导体赝能隙温度下的自发克尔效应大小预测，铜酸盐应表现出约0.1 Ohm⁻¹·cm⁻¹的反常霍尔效应。这是一个小值，但在实验可及范围内，我们鼓励对此进行探索。尽管我们的处理并非明确的量子几何，但与基于量子几何关系和有限物理信息对物理量设定界限的努力有一些相似之处。
英文摘要
Based on the Kramers-Krong relations, we derive and apply a quite general expression that that relates the low frequency quasi-dc Hall conductivity to the asymptotic high frequency optical Hall response (and its manifestations in Kerr and Faraday effects) for time-reversal symmetry breaking (TRSB) states of matter like ferromagnets and time-reversal symmetry breaking superconductors as well as metals in magnetic field. Parametric plots shows this relation is obeyed exactly for the trivial single-mode case of sharp cyclotron resonance, and approximately for theoretical models for ferromagnets and TRSB superconductors. We also apply it to the experimental data from a variety of ferromagnetic systems and show reasonable agreement there as well. We use the relation to predict, from the size of the spontaneous Kerr effect at the pseudogap temperature of the cuprate superconductors that cuprates should exhibit an anomalous Hall effect of approximately 0.1 Ohm$^{-1}\cdot$cm$^{-1}$. This is a small value, but one within experimental reach and we encourage the search for it. Although not explicitly quantum geometric, our treatment has some similarities to efforts to set bounds on physical quantities based on quantum geometric relations and limited physical information.
