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Orbital magnetism of graphene flakes

Orbital magnetism is studied for graphene flakes with various shapes and edge configurations using the tight-binding approximation. In the low-temperature regime where the thermal energy is much smaller than to the energy level spacing, the susceptibility rapidly changes between diamagnetism and paramagnetism as a function of Fermi energy, in accordance with the energy level structure. The susceptibility at charge neutral point is generally larger in armchair flake than in zigzag flake, and larger in hexagonal flake than in triangular flake. As the temperature increases, the discrete structures due to the quantum confinement are all gone, and the susceptibility approximates the bulk limit independently of the atomic configuration. The diamagnetic current circulates entirely on the graphene flake at zero temperature, while in increasing temperature it is localized near the edge with the characteristic depth proportional to 1/T. We predict that the diamagnetism of graphene can be observed using the alignment of graphene flakes in a feasible range of magnetic field.