For tilted type-I Weyl semimetals, our theoretical study indicates that the Kubo conductivity parallel to cone tilt direction increases rapidly with the Fermi energy. Hence it deviates from its Boltzmann counterpart sizably even though the electronic wavelength is so short that the quantum interference is seemingly trivial. As a result, such a system shows huge anisotropy of the conductivity. By means of the diagrammatic expansion technique, we find that the absence of backscattering and the breakdown of the time reversal symmetry in tilted Weyl semimetals are two crucial factors which bring about the nontrivial inter-band contribution to the Kubo conductivity. Our findings indicate that Boltzmann theory fails to describe reasonably the electronic transport of a tilted Weyl cone, even in the case of weak scattering and short Fermi wavelength. Though in this regime such a semiclassical transport theory is believed to be valid according to conventional arguments. This situation should be paid attention.

对于倾斜的 I 型外尔半金属，我们的理论研究表明，平行于锥体倾斜方向的 Kubo 电导率随着费米能量的增加而迅速增加。因此，即使电子波长如此之短以至于量子干涉看似微不足道，它也与玻尔兹曼对应物有相当大的偏差。结果，这样的系统显示出巨大的电导率各向异性。通过图解扩展技术，我们发现倾斜的外尔半金属中没有后向散射和时间反演对称性的破坏是导致对 Kubo 电导率的非平凡带间贡献的两个关键因素。我们的研究结果表明，即使在弱散射和短费米波长的情况下，玻尔兹曼理论也无法合理地描述倾斜的外尔锥的电子传输。尽管在这种情况下，根据传统的论点，这种半经典的传输理论被认为是有效的。这种情况应引起重视。