The quantum Hall effect in graphene samples and the relativistic Dirac effective action

We study the Euclidean effective action per unit area and the charge density for a Dirac field in a two--dimensional spatial region, in the presence of a uniform magnetic field perpendicular to the 2D--plane, at finite temperature and density. In the limit of zero temperature we reproduce, after performing an adequate Lorentz boost, the Hall conductivity measured for different kinds of graphene samples, depending upon the phase choice in the fermionic determinant.Comment: Conclusions extended. References added. 9 pages. 1 figur

Parity-odd effects and polarization rotation in graphene

We show that the presence of parity-odd terms in the conductivity (or, in other words, in the polarization tensor of Dirac quasiparticles in graphene) leads to rotation of polarization of the electromagnetic waves passing through suspended samples of graphene. Parity-odd Chern-Simons type contributions appear in external magnetic field, giving rise to a quantum Faraday effect (though other sources of parity-odd effects may also be discussed). The estimated order of the effect is well above the sensitivity limits of modern optical instruments.Comment: 8 page