Magneto-transport properties of gapped graphene

Based on the Kubo formula, we have studied the electron transport properties of a gapped graphene in the presence of a strong magnetic field. By solving the Dirac equation, we find that the Landau level spectra in two valleys differ from each other in that the n = 0 level in the K valley is located at top of the valence band, whereas it is at the bottom of the conduction band in the K' valley. Thus, in an individual valley, the symmetry between conduction and valence bands is broken by the presence of a magnetic field. By using the self-consistent Born approximation to treat the long range potential scattering, we formulate the diagonal and the Hall conductivities in terms of the Green function. To perform the numerical calculation, we find that a large bandgap can suppress the quantum Hall effect, owing to the enhancement of the bandgap squeezing the spacing between the low-lying Landau levels. On the other hand, if the bandgap is not very large, the odd integer quantum Hall effect experimentally, observed in the gapless graphene, remains in the gapped one. However, such a result does not indicate the half integer quantum Hall effect in an individual valley of the gapped graphene. This is because the heights of the Hall plateaux in either valley can be continuously tuned by the variation of the bandgap. More interestingly, we find that the height of the diagonal conductivity peak corresponding to the n = 0 Landau level is independent of the bandgap if the scattering is not very strong. In the weak scattering limit, we demonstrate analytically that such a peak takes a universal value e(2)/(hpi), regardless of the bandgap.