Singular orbital magnetism of graphene

The origin of the singular diamagnetic susceptibility at the Dirac point is probed through the study of effects of band-gap opening and spatially varying magnetic field. In the presence of a band gap, the susceptibility is nonzero only inside the band gap and exhibits a discrete jump at the band edges down to zero in the conduction and valence bands. The jump height is understood in terms of the pseudo-spin paramagnetism arising from valley degree of freedom. In spatially varying magnetic field with wave vector q , the susceptibility becomes nonzero only in a finite energy region containing the Dirac point, determined by q . This behavior is understood in terms of electronic states numerically calculated in periodic magnetic field.