Coulomb interaction effect in tilted Weyl fermion in two dimensions

TL;DR

This paper investigates how Coulomb interactions affect the velocities of tilted Weyl fermions in two dimensions, revealing velocity enhancement, isotropization, and Cherenkov radiation phenomena.

Contribution

It derives renormalization group equations for tilted Weyl fermions, showing Coulomb interactions lead to velocity increase and cone isotropization at low energies.

Findings

Velocities increase as energy decreases, approaching the speed of light.

System restores isotropic Weyl cone despite initial tilt.

Cherenkov radiation occurs when velocities reach the speed of light.

Abstract

Weyl fermions with tilted linear dispersions characterized by several different velocities appear in some systems including the quasi-two-dimensional organic semiconductor $\alpha$-(BEDT-TTF)$_2$I$_3$ and three-dimensional WTe$_2$. The Coulomb interaction between electrons modifies the velocities in an essential way in the low-energy limit, where the logarithmic corrections dominate. Taking into account the coupling to both the transverse and longitudinal electromagnetic fields, we derive the renormalization group equations for the velocities of the tilted Weyl fermions in two dimensions, and found that they increase as the energy decreases and eventually hit the speed of light $c$ to result in the Cherenkov radiation. Especially, the system restores the isotropic Weyl cone even when the bare Weyl cone is strongly tilted and the velocity of electrons becomes negative in certain directions.