Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach
Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach
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DOI：
10.1103/physrevb.75.045315
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发表时间：
2007-01-01
影响因子：
3.7
通讯作者：
Sinova, Jairo
中科院分区：
文献类型：
--
作者：
Sinitsyn, N. A.;MacDonald, A. H.;Sinova, Jairo
反常霍尔效应（AHE）是铁磁金属中自旋轨道耦合的结果，主要与密度矩阵对带指数非对角电场的响应有关。由于这个原因，混乱的贡献，AHE是很难处理系统使用半经典玻尔兹曼方程的方法，即使当弱本地化校正被忽略。在这篇文章中，我们明确地证明了一个适当修改的半经典输运理论，其中包括异常速度和侧跳的贡献和微观Kubo-Streda微扰理论的等价性，特别是非常规的贡献，在半经典理论确定特定的费曼图时，计算进行了带本征态表示。我们建立的等价性验证了明确的计算的情况下，二维狄拉克模型哈密顿相关的石墨烯。
The anomalous Hall effect (AHE) is a consequence of spin-orbit coupling in a ferromagnetic metal and related primarily to density-matrix response to an electric field that is off-diagonal in band index. For this reason disorder contributions to the AHE are difficult to treat systematically using a semiclassical Boltzmann equation approach, even when weak localization corrections are disregarded. In this article we explicitly demonstrate the equivalence of an appropriately modified semiclassical transport theory which includes anomalous velocity and side-jump contributions and microscopic Kubo-Streda perturbation theory, with particular unconventional contributions in the semiclassical theory identified with particular Feynman diagrams when calculations are carried out in a band-eigenstate representation. The equivalence we establish is verified by explicit calculations for the case of the two-dimensional Dirac model Hamiltonian relevant to graphene.