Longitudinal optical conductivities for tilted Weyl fermions in arbitrary dimensionality

The unified form of longitudinal optical conductivities (LOCs) for tilted Weyl fermions in arbitrary spatial dimensionality is 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 with respect to the tilting direction, and all the tilted phases. In addition, they automatically reproduce the analytical results of previous works for one-dimensional, two-dimensional, and three-dimensional tilted Weyl systems. Our work provides not only a once-for-all method prior to the one-by-one calculation of LOCs but also deep insights into the impacts of spatial dimensionality in the tilted Weyl fermions.