Coulomb interaction and magnetic catalysis in the quantum Hall effect in graphene

Details Coulomb interaction and magnetic catalysis in the quantum Hall effect in graphene Coulomb interaction and magnetic catalysis in the quantum Hall effect in graphene

2011-05-06

arxiv.org/abs/1105.1360v2

Phys. Scr. T 146 (2012) 014018

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

22 pages, 5 figures; Final version published in the Proceedings of the 2010 Nobel Symposium on Graphene and Quantum Matter

Scientific paper

10.1088/0031-8949/2012/T146/0140

The dynamics of symmetry breaking responsible for lifting the degeneracy of the Landau levels in the integer quantum Hall effect in graphene is studied in a low-energy model with the Coulomb interaction. The gap equation for Dirac quasiparticles is analyzed for both the lowest and higher Landau levels, taking into account the Landau levels mixing. It is shown that the characteristic feature of the long-range Coulomb interaction is the decrease of the gap parameters with increasing the Landau level index $n$ ("running" gaps). The renormalization (running) of the Fermi velocity as a function of $n$ is also studied. The solutions of the gap equation reproduce correctly the experimentally observed integer quantum Hall plateaus in graphene in strong magnetic fields.

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