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
2 Faculdade de Física, Universidade Federal do Pará, Avenida Augusto Correa 01, 66075-110 Belém, Pará, Brazil
Received in final form: 20 October 2016
Published online: 12 December 2016
The experimental observation of the renormalization of the Fermi velocity vF 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.
Key words: Mesoscopic and Nanoscale Systems
© The Author(s) 2016. This article is published with open access at Springerlink.com
This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.