We present a unified theory of charge carrier transport in 2D Dirac systems with broken mirror inversion and time-reversal symmetries (e.g., as realized in ferromagnetic graphene). We find that the entanglement between spin and pseudospin SU(2) degrees of freedom stemming from spin-orbit effects leads to a distinctive gate voltage dependence (change of sign) of the anomalous Hall conductivity approaching the topological gap, which remains robust against impurity scattering and thus is a smoking gun for magnetized 2D Dirac fermions. Furthermore, we unveil a robust skew scattering mechanism, modulated by the spin texture of the energy bands, which causes a net spin accumulation at the sample boundaries even for spin-transparent disorder. The newly unveiled extrinsic spin Hall effect is readily tunable by a gate voltage and opens novel opportunities for the control of spin currents in 2D ferromagnetic materials.

中文翻译：

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二维Dirac材料中的异常霍尔效应

我们提出了二维Dirac系统中电荷载流子传输的统一理论，该系统具有破碎的镜面反转和时间反转对称性（例如，在铁磁石墨烯中实现）。我们发现，自旋轨道效应引起的自旋和伪自旋SU（2）自由度之间的纠缠导致异常霍尔电导率接近拓扑间隙的独特的栅极电压依赖性（符号变化），对杂质散射仍然具有鲁棒性因此是一种用于磁化2D Dirac费米子的烟枪。此外，我们揭示了一种强大的偏斜散射机制，该机制受能带的自旋纹理调制，即使对于自旋透明无序现象，也会在样品边界处引起净自旋累积。