Collective effects in tilted Weyl cones: Optical conductivity, polarization, and Coulomb interactions reshaping the cone

Recently, the existence of Dirac/Weyl cones in three-dimensional systems has been demonstrated experimentally. While in high-energy physics the isotropy of the Dirac/Weyl cones is guaranteed by relativistic invariance, in condensed-matter systems corrections to this can occur, with one possible type being a tilt. In this paper, we study the effect of tilted Weyl cones in collective effects. We study both the optical conductivity as well as the polarization function. We also investigate the perturbative effect of long-range Coulomb interactions using a renormalization-group calculation. We find that the tilt is perturbatively renormalized towards zero and at low energies the system flows to an effectively untilted theory.