The polar Kerr effect in superconducting ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ implies finite ac anomalous Hall conductivity. Since intrinsic anomalous Hall effect (AHE) is not expected for a chiral superconducting pairing developed on the single Ru $d_{xy}$ orbital, multiorbital chiral pairing actively involving the Ru $d_{xz}$ and $d_{yz}$ orbitals has been proposed as a potential mechanism. Here we propose that AHE could still arise even if the chiral superconductivity is predominantly driven by the $d_{xy}$ orbital. This is demonstrated through two separate models which take into account subdominant orbitals in the Cooper pairing, one involving the oxygen $p_x$ and $p_y$ orbitals in the $\mathrm{Ru}{\mathrm{O}}_2$ plane, and another the $d_{xz}$ and $d_{yz}$ orbitals. In both models, finite orbital mixing between the dominant $d_{xy}$ and the other orbitals may induce interorbital pairing between them, and the resultant states support intrinsic AHE, with Kerr rotation angles that could potentially reconcile with the experimental observation. Our proposal therefore sheds new light on the microscopic pairing in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. We also show that intrinsic Hall effect is generally absent for nonchiral states such as $\mathcal{S}+i\mathcal{D}, \mathcal{D}+i\mathcal{P}$, and $\mathcal{D}+i\mathcal{G}$, which provides a clear constraint on the symmetry of the superconducting order in this material.

中文翻译：

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具有手性超导电性的Sr2RuO4中的隐性异常霍尔效应

超导中的极性克尔效应 $r_2{O}_4$意味着有限的交流异常霍尔电导率。由于对于单个Ru上形成的手性超导对，预期不存在固有的异常霍尔效应（AHE）$d_{Xÿ}$ 参与Ru的轨道，多轨道手性配对 $d_{Xž}$ 和 $d_{ÿž}$有人提出将轨道作为一种潜在的机制。在这里，我们提出即使手性超导主要由氢原子驱动，AHE仍然可能出现。$d_{Xÿ}$轨道。这是通过两个独立的模型证明的，这些模型考虑了库珀配对中的主要轨道，其中一个涉及氧$p_X$ 和 $p_{ÿ}$ 在轨道 $茹{\mathrm{Ø}}_2$ 飞机，另一个 $d_{Xž}$ 和 $d_{ÿž}$轨道。在这两个模型中，主要轨道之间的有限轨道混合$d_{Xÿ}$其他轨道可能会在它们之间引起轨道间配对，并且所得状态支持本征AHE，其Kerr旋转角可能与实验观察相符。因此，我们的建议为显微配对提供了新的思路。$r_2{O}_4$。我们还表明，对于非手性状态，例如，通常没有内在霍尔效应$\mathcal{小号}+\mathrm{一世}\mathcal{d}， \mathcal{d}+\mathrm{一世}\mathcal{P}$和 $\mathcal{d}+\mathrm{一世}\mathcal{G}$，这对这种材料中超导阶的对称性提供了明确的约束。