Longitudinal optical conductivities of tilted Weyl fermions in arbitrary dimensionality

TL;DR

This paper derives a unified analytical expression for the longitudinal optical conductivities of tilted Weyl fermions across arbitrary dimensions, encompassing various doping and tilt conditions, and reveals universal fixed points.

Contribution

It provides a comprehensive, dimension-independent analytical framework for LOCs in tilted Weyl fermions, extending previous results and offering new insights into their dimensional effects.

Findings

Unified analytical expressions for LOCs in arbitrary dimensions.

Reproduction of known results in 1D, 2D, and 3D cases.

Identification of a universal fixed point at  for tilted Dirac bands.

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.