Orbital magnetic susceptibility of finite-sized graphene

We study the orbital magnetism of graphene ribbon in the effective-mass approximation, to figure out the finite-size effect on the singular susceptibility known in the bulk limit. We find that the susceptibility at T=0 oscillates between diamagnetism and paramagnetism as a function of _F, in accordance with the subband structure formed by quantum confinement. In increasing T, the oscillation rapidly disappears once the thermal broadening energy exceeds the subband spacing, and the susceptibility χ( _F) approaches the bulk limit, i.e., a thermally broadened diamagnetic peak centered at _F=0. The electric current supporting the diamagnetism is found to flow near the edge with a depth ∼v/(2πk _BT), with v being the band velocity, while at T=0 the current distribution spreads entirely in the sample reflecting the absence of the characteristic wavelength in graphene. The result is applied to estimate the three-dimensional random-stacked multilayer graphene, where we show that the external magnetic field is significantly screened inside the sample in low temperatures, in a much stronger manner than in graphite.