Quantum critical scaling in magnetic field near the Dirac point in graphene

Graphene, a monolayer of graphite, exhibits some peculiar electronic properties which are consequences of the pseudo relativistic Dirac like excitations. The anomalous integer quantum Hall effect, i. e. platoues in Hall conductivity $\sigma_{xy}$ at filling factors $f=\pm(4 n+2)$, which can be understood within the framework of non-interacting Dirac like quasiparticles is one of such. On the other hand, the appearance of additional Hall states at filling factors $f=0$ and $f=\pm 1$ at higher magnetic fields calls for electron-electron interactions to be taken into account. Motivated by the recent measurement of the activation energy at the quantum Hall state at the filling factor $f =1$ in graphene, I will discuss the scaling of the interaction-induced gaps in the vicinity of the Dirac point with the magnetic field. The gap at $f =1$ is shown to be bounded from above by $E(1)/C$, where $E(n)={v_F}\sqrt{2nB}$ is the Landau-level energy and $C=5.985+O{1/N}$ is a universal number. The universal scaling functions computed exactly for a large number of Dirac fermions N will also be presented. The sublinear dependence of the gap at the laboratory fields of $10 T