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

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.

Discussion about the fermionic mass has been added to the previous version

References in corpus (3)

• Electric Field Effect in Atomically Thin Carbon Films
• Interaction phenomena in graphene seen through quantum capacitance
• Graphene via large N I: Renormalization

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• Many-body renormalization of Landau levels in graphene due to screened Coulomb interaction
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• Projected Proca Field Theory: a One-Loop Study
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