论文标题
相位空间浆果曲率的异常和拓扑厅效应的统一理论
Unified Theory of the Anomalous and Topological Hall Effects with Phase Space Berry Curvatures
论文作者
论文摘要
除了普通的霍尔电阻外，手性磁体中的霍尔实验通常被分析为以动量浆果曲率为主的异常霍尔效应的总和，由动量空间浆果曲率和拓扑厅效应分析。这就提出了一个问题，即如何在相等的基础上合并异常速度的效果和磁化的真实空间绕组，以及当电阻率的这种分解是合理的。我们通过在半古典方法中包括全相空间浆果曲率的影响，并通过在弱自旋轨道耦合方案中求解玻尔兹曼方程时，为这些问题提供明确的答案，当时磁化强度纹理在平均自由路径的规模上缓慢变化。我们表明，大厅的电阻率只是异常和拓扑贡献的总和，并从浆果曲率独立的和混合曲率项中校正可忽略不计。我们还使用精确的kubo形式主义来数字研究无限均值路径的相反极限，并表明结果与半古典结果相似。
Hall experiments in chiral magnets are often analyzed as the sum of an anomalous Hall effect, dominated by momentum-space Berry curvature, and a topological Hall effect, arising from the real-space Berry curvature in the presence of skyrmions, in addition to the ordinary Hall resistivity. This raises the questions of how one can incorporate, on an equal footing, the effects of the anomalous velocity and the real space winding of the magnetization, and when such a decomposition of the resistivity is justified. We provide definitive answers to these questions by including the effects of all phase-space Berry curvatures in a semi-classical approach and by solving the Boltzmann equation in a weak spin-orbit coupling regime when the magnetization texture varies slowly on the scale of the mean free path. We show that the Hall resistivity is then just the sum of the anomalous and topological contributions, with negligible corrections from Berry curvature-independent and mixed curvature terms. We also use an exact Kubo formalism to numerically investigate the opposite limit of infinite mean path, and show that the results are similar to the semi-classical results.
