The anomalous spin Hall conductivity in the holographic model of Dirac semimetals with two Dirac nodes protected by the crystal symmetry has been elaborated. Such a system besides the chiral anomaly possesses another anomaly that is related to the ${\mathbb{Z}}_2$ topological charge of the system. The holographic model of the system contains matter action with two $U(1)$-gauge fields as well as the appropriate combination of the Chern-Simons gauge terms. We also allow for the coupling of two gauge fields via the kinetic mixing parametrized by the coupling $\alpha$. The holographic approach in the probe limit enables us to obtain Hall conductivity. The aim of this work is to describe the phase transitions in the ${\mathbb{Z}}_2$ Dirac semimetals between the topologically trivial and nontrivial phases. Interestingly the anomalous Hall conductivity plays a role of the order parameter of this phase transition. The holographically found prefactor of the Hall conductivity in the topologically nontrivial phase depends on the coupling $\alpha$ and the Chern-Simons couplings.

中文翻译：

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全息Z2Dirac半金属的反常霍尔电导率

已经详细阐述了具有两个受晶体对称性保护的狄拉克节点的狄拉克半金属全息模型中的异常自旋霍尔电导率。除了手性异常之外，这样的系统还具有与${\mathbb{Z}}_2$系统的拓扑荷。系统的全息模型包含两个物质作用$你(1)$-规范场以及Chern-Simons规范项的适当组合。我们还允许通过耦合参数化的动力学混合来耦合两个规范场$\alpha$. 探针极限中的全息方法使我们能够获得霍尔电导率。这项工作的目的是描述相变${\mathbb{Z}}_2$拓扑平凡和非平凡相之间的狄拉克半金属。有趣的是，异常霍尔电导率在此相变的有序参数中起着重要作用。拓扑非平凡相中霍尔电导率的全息前因数取决于耦合$\alpha$ 和陈 - 西蒙斯耦合。