Functional renormalization group approach to interacting three-dimensional Weyl semimetals

TL;DR

This paper uses a functional renormalization group approach to analyze how long-range Coulomb interactions affect the quasiparticle properties and dielectric function of three-dimensional Weyl semimetals, extending previous static results.

Contribution

It introduces a FRG method with two cutoff schemes to compute dynamic screening effects and quasiparticle velocities for Weyl semimetals with multiple nodes.

Findings

Quasiparticle velocity exhibits logarithmic momentum dependence.

Dielectric function agrees with classical results in static limit.

Dynamic screening modifies wave function renormalization.

Abstract

We investigate the effect of long-range Coulomb interaction on the quasiparticle properties and the dielectric function of clean three-dimensional Weyl semimetals at zero temperature using a functional renormalization group (FRG) approach. The Coulomb interaction is represented via a bosonic Hubbard-Stratonovich field which couples to the fermionic density. We derive truncated FRG flow equations for the fermionic and bosonic self-energies and for the three-legged vertices with two fermionic and one bosonic external legs. We consider two different cutoff schemes --- cutoff in fermionic or bosonic propagators --- in order to calculate the renormalized quasiparticle velocity and the dielectric function for an arbitrary number of Weyl nodes and the interaction strength. If we approximate the dielectric function by its static limit, our results for the velocity and the dielectric function are in good agreement with that of A. A. Abrikosov and S. D. Beneslavski{\u{i}} [Sov. Phys. JETP \textbf{32}, 699 (1971)] exhibiting slowly varying logarithmic momentum dependence for small momenta. We extend their result for an arbitrary number of Weyl nodes and finite frequency by evaluating the renormalized velocity in the presence of dynamic screening and calculate the wave function renormalization.