We study the effect of electron interaction on the spin splitting and the $g$ factor in graphene in a perpendicular magnetic field using the Hartree and the Hubbard approximations within the Thomas-Fermi model. We found that the effective $g$ factor is enhanced in comparison to its free-electron value $g=2$ and oscillates as a function of the filling factor $\nu$ in the range $2\le g^{*}\lesssim 4$ reaching maxima at $\nu =4N=0,\pm 4,\pm 8,...$ and minima at $\nu =4\left(N+\frac{1}{2}\right)=\pm 2,\pm 6,\pm 10,...$, with $N$ being the Landau level index. We outline the role of charged impurities in the substrate, which are shown to suppress the oscillations of the $g^{*}$ factor. This effect becomes especially pronounced with the increase of the impurity concentration, when the effective $g$ factor becomes independent of the filling factor, reaching a value of $g^{*}\approx 2.3$. A relation to the recent experiment is discussed.

• Received 2 August 2012

DOI:https://doi.org/10.1103/PhysRevB.86.155440