含位错Weyl半金属的扭转响应和Liouville反常
Torsional Responses and Liouville Anomaly in Weyl Semimetals with Dislocations
摘要：
三维Weyl半金属中的Weyl节点破坏了Liouville方程，导致了Liouville反常。本文从量子场论出发，将Wigner变换与带投影操作相结合，导出了Weyl费米子在电磁场和挠率作用下的半经典作用量和运动方程。结果表明，Liouville反常与轴向规范场完全不同，它包括一个新的纯挠率反常项、一个电磁场与挠率的混合项以及一个常规的手征反常项。我们发现了各种扭转响应，再现了手征涡旋效应和扭转手征磁效应。预测了一种新的扭转修正的反常霍尔效应，它是由于刘维反常中的混合项引起的，并讨论了它的实现。因此，我们的工作不仅提供了新的见解外尔费米子的扭转响应，但也作为一个出发点，研究其拓扑响应。
英文摘要：
Weyl nodes in three-dimensional Weyl semimetals break the Liouville equation, leading to the Liouville anomaly. Here we present a new approach to derive the semiclassical action and equations of motion for Weyl fermions in the presence of electromagnetic fields and torsions from the quantum field theory: combining the Wigner transformation with band projection operation. It has been shown that the Liouville anomaly, including a new pure torsion anomaly term, a mixing term between the electromagnetic fields and torsions as well as the conventional chiral anomaly, entirely differs from the counterpart of axial gauge fields. We find various torsional responses and reproduce the chiral vortical effect and the torsional chiral magnetic effect. A new torsion modified anomalous Hall effect due to the mixing term in the Liouville anomaly is predicted and its implementation is also discussed. Therefore, our work not only provides new insights into the torsional responses for Weyl fermions but also acts as a starting point to investigate their topological responses.
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