Many-body effects and ultraviolet renormalization in three-dimensional Dirac materials

TL;DR

This paper develops a detailed many-body theory for 3D Dirac materials, analyzing ultraviolet renormalization effects on key parameters and revealing a critical interaction strength influencing low-energy behavior.

Contribution

It provides the first comprehensive second-order analysis of interaction effects and ultraviolet renormalization in 3D Dirac semimetals, including velocity and coupling flow corrections.

Findings

Identification of a critical coupling where interaction strength grows at low energies.

Discovery of non-monotonic Fermi velocity behavior near the non-interacting fixed point.

Higher-order corrections are small but significant for materials with many electron flavors.

Abstract

We develop a theory for electron-electron interaction-induced many-body effects in three dimensional (3D) Weyl or Dirac semimetals, including interaction corrections to the polarizability, electron self-energy, and vertex function, up to second order in the effective fine structure constant of the Dirac material. These results are used to derive the higher-order ultraviolet renormalization of the Fermi velocity, effective coupling, and quasiparticle residue, revealing that the corrections to the renormalization group (RG) flows of both the velocity and coupling counteract the leading-order tendencies of velocity enhancement and coupling suppression at low energies. This in turn leads to the emergence of a critical coupling above which the interaction strength grows with decreasing energy scale. In addition, we identify a range of coupling strengths below the critical point in which the Fermi velocity varies non-monotonically as the low-energy, non-interacting fixed point is approached. Furthermore, we find that while the higher-order correction to the flow of the coupling is generally small compared to the leading order, the corresponding correction to the velocity flow carries an additional factor of the Dirac cone flavor number (the multiplicity of electron species, e.g. ground-state valley degeneracy arising from the band structure) relative to the leading-order result. Thus, for materials with a larger multiplicity, the regime of velocity non-monotonicity is reached for modest values of the coupling strength.