Burkov A A, Balents Leon
Department of Physics, University of California, Santa Barbara, California 93106, USA.
Phys Rev Lett. 2003 Aug 1;91(5):057202. doi: 10.1103/PhysRevLett.91.057202. Epub 2003 Jul 30.
We present a theory of the anomalous Hall effect in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conductivity sigma(AH)(xy). We show that sigma(AH)(xy) is proportional to the first derivative of the density of states varrho(epsilon) and thus can be expected to change sign as a function of impurity band filling. We also show that sigma(AH)(xy) depends on temperature as the longitudinal conductivity sigma(xx) within logarithmic accuracy.
我们提出了一种关于铁磁体（Ga，Mn）As中反常霍尔效应的理论，该理论适用于传导是由于杂质带中局域态之间空穴的声子辅助跳跃的情况。我们表明，该系统中反常霍尔电导率的微观起源可归因于一个相位，即空穴在存在自旋轨道相互作用和局域Mn磁矩的背景磁化时绕闭环路径跳跃时所获得的相位。将该问题映射到一个随机电阻网络，我们推导出了宏观反常霍尔电导率σ(AH)(xy)的解析表达式。我们表明，σ(AH)(xy)与态密度ρ(ε)的一阶导数成正比，因此可以预期它会随着杂质带填充而改变符号。我们还表明，在对数精度范围内，σ(AH)(xy)与纵向电导率σ(xx)一样依赖于温度。
