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 ${\varepsilon }_F$, 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 $\chi \left({\varepsilon }_F\right)$ approaches the bulk limit, i.e., a thermally broadened diamagnetic peak centered at ${\varepsilon }_F=0$. The electric current supporting the diamagnetism is found to flow near the edge with a depth $\sim \hslash v/\left(2\pi k_{B}T\right)$, 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.

• Received 31 January 2012

DOI:https://doi.org/10.1103/PhysRevB.85.165454