Anomaly related transport of Weyl fermions for Weyl semi-metals
Karl Landsteiner
备注：
v3: 24 pages, substantially improved discussion of CME. Distinction of covariant and consistent forms of the current. CME appears as anomalous charge accumulation on the edges for the covariant current
We present a field theoretical model of anomalous transport in Weyl semi-metals. We calculate the Chiral Magnetic and Chiral Vortical Effect in the electric, axial (valley) and energy current. Our findings coincide with the results of a recent analysis using kinetic theory in the bulk of the material. We point out that the kinetic currents have to be identified with the covariant currents in quantum field theory. These currents are anomalous and the CME appears as anomalous charge creation/annihilation at the edges of the Weyl semi-metal. We discuss a possible simultaneous experimental test of the chiral magnetic and the chiral vortical effect sensitive to the temperature dependence induce by the gravitational contribution to the axial anomaly.
Weyl semimetals possess massless chiral quasi-particles, and are thus affected by the triangle anomalies. We discuss the features of the chiral magnetic and chiral vortical effects specific to Weyl semimetals, and then propose three novel phenomena caused by the triangle anomalies in this material: 1) anomaly cooling; 2) charge transport by soliton waves as described by the Burgers' equation, and 3) the shift of the BKT phase transition of superfluid vortices coupled to Weyl fermions. In addition, we establish the conditions under which the chiral magnetic current exists in real materials.
Universidad Autónoma de Madrid（马德里自治大学）；IFT-UAM/CSIC（理论物理研究所（马德里自治大学/西班牙高等科学研究委员会））；Simons Center for Geometry and Physics, State University of New York Stony Brook（纽约州立大学石溪分校西蒙斯几何与物理中心）；CERN（欧洲核子研究组织）；Universidad Complutense de Madrid (UCM)（马德里康普顿斯大学）
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Zhejiang Ocean University（浙江海洋大学）；University of Science and Technology of China（中国科学技术大学）；Shandong University（山东大学）；Joint Institute for Nuclear Research（苏联联合核研究所）；NRC Kurchatov Institute（库尔恰托夫国家研究中心）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）
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Recently it is found that Weyl anomaly leads to new anomalous currents in an external electromagnetic field in the curved spacetime. For simplicity, the initial works mainly focus on weak gravitational fields and the anomalous current is obtained for conformally flat spaces with small scale factors. In this paper, we generalize the results to the case with arbitrary scale factors. Firstly, we derive the transformation law of current under Weyl transformation, from which one can read off the anomalous current in general conformally flat spaces. Secondly, by using the Weyl transformation of curr…
