Eur. Phys. J. B (2016) 89: 271
https://doi.org/10.1140/epjb/e2016-70606-4

Regular Article

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

¹ Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584CC Utrecht, The Netherlands
² Faculdade de Física, Universidade Federal do Pará, Avenida Augusto Correa 01, 66075-110 Belém, Pará, Brazil

^a e-mail: C.demoraissmith@uu.nl

Received: 13 October 2016
Received in final form: 20 October 2016
Published online: 12 December 2016

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 for the massive case arises due to electronic interactions. In addition, for gapped systems, we observe a running of the mass parameter.