The influence of a weak magnetic field in the Renormalization-Group functions of (2+1)-dimensional Dirac systems

TL;DR

This paper demonstrates that weak perpendicular magnetic fields do not alter the renormalization-group functions of (2+1)-dimensional Dirac systems, confirming that electronic interactions primarily drive Fermi velocity renormalization in graphene.

Contribution

The study clarifies the effect of weak magnetic fields on RG functions in Dirac systems using PQED formalism, extending previous results to include magnetic field effects.

Findings

Weak magnetic fields do not change RG functions for Fermi velocity.

Interactions are the main factor in Fermi velocity renormalization.

Gapped systems show a running mass parameter.

Abstract

The experimental observation of the renormalization of the Fermi velocity $v_{F}$ as a function of doping has been a landmark for confirming the importance of electronic interactions in graphene. Although the experiments were performed in the presence of a perpendicular magnetic field $B$, the measurements are well described by a renormalization-group (RG) theory that did not include it. Here we clarify this issue, for both massive and massless Dirac systems, and show that for the weak magnetic fields at which the experiments are performed, there is no change in the renormalization-group functions. Our calculations are carried out in the framework of the Pseudo-quantum electrodynamics (PQED) formalism, which accounts for dynamical interactions. We include only the linear dependence in $B$, and solve the problem using two different parametrizations, the Feynman and the Schwinger one. We confirm the results obtained earlier within the RG procedure and show that, within linear order in the magnetic field, the only contribution to the renormalization of the Fermi velocity arises due to interactions. In addition, for gapped systems, we observe a running of the mass parameter.