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.
|ジャーナル||Physical Review B - Condensed Matter and Materials Physics|
|出版ステータス||Published - 2012 4月 30|
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