Integral quantum Hall effect in graphene: Zero and finite Hall field

Abstract

We study the influence of a finite Hall field EH on the Hall conductivity σyx in graphene. Analytical expressions are derived for σyx using the Kubo-Greenwood formula. For vanishing EH, we obtain the well-known expression σyx=4(N+1/ 2)e2/h. The inclusion of the dispersion of the energy levels, previously not considered, and their width, due to scattering by impurities, produces the plateau of the n=0 Landau level. Further, we evaluate the longitudinal resistivity ρxx and show that it exhibits an oscillatory behavior with the electron concentration. The peak values of ρxx depend strongly on the impurity concentration and their potential. For a finite E H, the result for σyx is the same as that for E H=0, provided EH is not strong, but the values and positions of the resistivity maxima are modified due to the E H-dependent dispersion of the energy levels. © 2011 American Physical Society.