Longitudinal optical conductivities of tilted Weyl fermions in arbitrary dimensionality

Abstract: The unified form of longitudinal optical conductivities (LOCs) in the tilted Weyl fermions for arbitrary spatial dimensionality are analytically calculated and expressed in terms of the joint density of state. The results are valid for both undoped and doped cases, both parallel and perpendicular components, and all the tilted phases. In addition, they reproduce analytical results of previous works for one-dimensional, two-dimensional, and three-dimensional tilted Weyl systems. The robust fixed point $\Gamma_{\chi}^{(\mathrm{IB})}(\omega=2\mu,d\ge 2;\mu,0<t\le 2)=1/2$ is universal for tilted Dirac bands in arbitrary spatial dimensionality. Our work provides not only a once-for-all method prior to the one-by-one calculation of the LOCs but also offer deep insights into the impacts of dimensionality in the tilted Weyl fermions.