Dielectric Function, Friedel Oscillation and Plasmons in Weyl Semimetals

We calculate the dielectric function of a Weyl semimetal at arbitrary momentum q and frequency ω within the random-phase approximation. Taking the static limit, we calculated the Friedel oscillation and found that: (1) For a single Weyl point, the oscillation ~ sin (2kFr)/r4 falls off faster by an 1/r factor than the one in traditional 3D systems ~ cos (2kFr)/r3. This difference arises from the suppression of backward scattering in Weyl fermion systems; (2) For Weyl semimetal with two Weyl points, there are additional oscillations decaying as cos (Q ⋅ r)/r3 and cos (Q ± 2kF) ⋅ r/r3, where Q is the momentum difference between the two Weyl points. We also calculated the plasmon dispersion and found features distinct from those of conventional 3D metals.