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Chiral anomaly, dimensional reduction, and magnetoresistivity of Weyl and Dirac semimetals

机译：Weyl和Dirac半金属的手征异常，尺寸减小和磁电阻率

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By making use of the Kubo formula, we calculate the conductivity of Dirac and Weyl semimetals in a magnetic field. We find that the longitudinal (along the direction of the magnetic field) magnetoresistivity is negative at sufficiently large magnetic fields for both Dirac and Weyl semimetals. The physical reason of this phenomenon is intimately connected with the dimensional spatial reduction 3 → 1 in the dynamics of. the lowest Landau level. The off-diagonal component of the transverse (with respect to the direction of the magnetic field) conductivity in Weyl semimetals contains an anomalous contribution directly proportional to the momentum-space separation between the Weyl nodes. This contribution comes exclusively from the lowest Landau level and, as expected, is independent of the temperature, chemical potential, and magnetic field. The other part of the off-diagonal conductivity is the same as in Dirac semimetals and is connected with a nonzero density of charge carriers. The signatures for experimental distinguishing Weyl semimetals from Dirac ones through the measurements of conductivity are discussed.
机译：通过使用久保公式，我们可以计算出狄拉克和魏尔半金属在磁场中的电导率。我们发现，对于Dirac和Weyl半金属，在足够大的磁场下，纵向（沿磁场的方向）磁阻为负。这种现象的物理原因与动力学的空间缩减3→1密切相关。最低的兰道水平。 Weyl半金属中的横向（相对于磁场方向）电导率的非对角线分量包含与Weyl节点之间的动量空间分隔成正比的异常贡献。这种贡献完全来自最低的朗道水平，并且与预期的温度，化学势和磁场无关。非对角线电导率的另一部分与狄拉克半金属相同，并与非零密度的载流子相连。讨论了通过电导率的测量将Weyl半金属与Dirac金属区别开来的特征。

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