Quantum Hall effect in graphene: A functional determinant approach

Details Quantum Hall effect in graphene: A functional determinant approach Quantum Hall effect in graphene: A functional determinant approach

2007-10-25

arxiv.org/abs/0710.4928v2

J.Phys.A41:164035,2008

Physics

High Energy Physics

High Energy Physics - Theory

Talk given at QFEXT07, Leipzig, Germany; discussion on the connection between phase of the determinant, Chern Simons and Berry

Scientific paper

10.1088/1751-8113/41/16/164035

We start the paper with a brief presentation of the main characteristics of graphene, and of the Dirac theory of massless fermions in 2+1 dimensions obtained as the associated low-momentum effective theory, in the absence of external fields. We then summarize the main steps needed to obtain the Hall conductivity in the effective theory at finite temperature and density, with emphasis on its dependence on the phase of the Dirac determinant selected during the evaluation of the effective action. Finally, we discuss the behavior, under gauge transformations, of the contribution due to the lowest Landau level, and interpret gauge transformations as rotations of the corresponding spinors around the magnetic field.

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