Polarization, plasmon, and Debye screening in doped 3D ani-Weyl semimetal

We compute the polarization function in a doped three-dimensional anisotropic-Weyl semimetal, in which the fermion energy dispersion is linear in two components of the momenta and quadratic in the third. Through detailed calculations, we find that the long wavelength plasmon mode depends on the fermion density $n_e$ in the form $\Omega_{p}^{\bot}\propto n_{e}^{3/10}$ within the basal plane and behaves as $\Omega_{p}^{z}\propto n_{e}^{1/2}$ along the third direction. This unique characteristic of the plasmon mode can be probed by various experimental techniques, such as electron energy-loss spectroscopy. The Debye screening at finite chemical potential and finite temperature is also analyzed based on the polarization function.