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

## TL;DR

This paper investigates how tilt in Weyl cones affects their optical and collective properties, showing that Coulomb interactions tend to reduce tilt, leading to an effectively untilted system at low energies.

## Contribution

It provides a detailed analysis of the impact of tilt on optical conductivity, polarization, and Coulomb interactions in Weyl semimetals, revealing tilt renormalization effects.

## Key findings

- Tilt is renormalized towards zero by Coulomb interactions.
- At low energies, the system behaves as if the Weyl cones are untilted.
- Tilt influences collective effects but diminishes under renormalization.

## Abstract

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, one possible type being a tilt. In this paper we study the effect of of tilted Weyl cones in collective effects. We study both the opticql 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.