Within the theoretical framework of Kubo linear response theory as well as the self-consistent Born approximation(SCBA), we perform a comparative study about the Hall conductivities of a Dirac semimetal(DSM) subject to, respectively, the intra- and inter-valley scattering. By calculating the Hall conductivity as a function of Fermi level, we find that when the Fermi level lies in the region around the Dirac node, the Hall conductivities between the two cases, i.e. subject to intra- and inter-valley scattering respectively, do not show appreciable difference, regardless of the scattering strength. As the Fermi level goes away from the Dirac node, the Hall conductivity in the case of inter-valley scattering is smaller than that in the case of intra-valley scattering if the scattering has relatively weak or moderate strength. In contrast, as scattering strength increases further, the Hall conductivity spectra between the two cases look almost identical no matter whether the Fermi level is close to or far away from the Dirac node. The underlying physics of these numerical results is that the Fermi surface has nontrivial contribution to the Hall conductivity in the case of weak or moderate scattering. However, in the case of strong scattering, it becomes much smaller than the contribution arising from all the occupied states. In addition, our study indicates that the cone tilt brings about the effective enhancement of Hall conductivity of DSMs.

在久保线性响应理论的理论框架以及自洽Born近似（SCBA）的基础上，我们对Dirac半金属（DSM）分别受谷内和谷间的霍尔电导率进行了比较研究。散射。通过将霍尔电导率作为费米能级的函数进行计算，我们发现，当费米能级位于狄拉克节点附近时，两种情况之间的霍尔电导率（即分别受到谷内和谷间散射的影响）不会不管散射强度如何，都显示出明显的差异。当费米能级远离Dirac节点时，如果散射具有相对较弱或中等的强度，则谷间散射情况下的霍尔电导率要小于谷内散射情况下的霍尔电导率。相比之下，随着散射强度的进一步提高，两种情况之间的霍尔电导率谱看起来几乎相同，无论费米能级是接近还是远离狄拉克节点。这些数值结果的基本物理原理是，在弱散射或中等散射的情况下，费米表面对霍尔电导率的贡献微不足道。但是，在强散射的情况下，它变得比所有占据状态引起的贡献小得多。此外，我们的研究表明，圆锥倾斜带来了DSMs霍尔电导率的有效增强。这些数值结果的基本物理原理是，在弱散射或中等散射的情况下，费米表面对霍尔电导率的贡献微不足道。但是，在强散射的情况下，它变得比所有占据状态引起的贡献小得多。此外，我们的研究表明，圆锥倾斜带来了DSMs霍尔电导率的有效增强。这些数值结果的基本物理原理是，在弱散射或中等散射的情况下，费米表面对霍尔电导率的贡献微不足道。但是，在强散射的情况下，它变得比所有占据状态引起的贡献小得多。此外，我们的研究表明，圆锥倾斜带来了DSMs霍尔电导率的有效增强。