The effect of the magnetic impurities on the charge transport in a magnetic topological ultra-thin film (MTF) is analytically investigated by applying the semi-classical Boltzmann framework through a modified relaxation-time approximation. Our results for the relaxation time of electrons as well as the charge conductivity of the system exhibit two distinct regimes of transport. We show that the generated charge current in a MTF is always dissipative and anisotropic when both conduction bands are involved in the charge transport. The magnetic impurities induce a chirality selection rule for the transitions of electrons which can be altered by changing the orientation of the magnetic impurities. On the other hand, when a single conduction band participates in the charge transport, the resistivity is isotropic and can be entirely suppressed due to the corresponding chirality selection rule. Our findings propose a method to determine an onset thickness at which a crossover from a three-dimensional magnetic topological insulator to a (two-dimensional) MTF occurs.

通过应用半经典玻尔兹曼骨架，通过改进的弛豫时间近似方法，分析研究了磁性杂质对磁性拓扑超薄膜（MTF）中电荷传输的影响。我们的电子弛豫时间以及系统的电荷电导率结果显示出两种不同的传输方式。我们表明，当两个导带都参与电荷传输时，MTF中产生的电荷电流总是耗散且各向异性的。磁性杂质诱导了电子跃迁的手性选择规则，该规则可以通过改变磁性杂质的取向来改变。另一方面，当单个导带参与电荷传输时，电阻率是各向同性的，并且由于相应的手性选择规则而可以完全抑制。我们的发现提出了一种确定起始厚度的方法，在起始厚度处会发生从三维磁性拓扑绝缘体到（二维）MTF的交叉。