Orbital magnetism of graphene nanostructures

We study the orbital magnetism of graphene ribbons and graphene flakes with various shapes and edge configurations. The property is significantly different depending on the relative magnitude of the thermal broadening energy ^kBT to the characteristic level spacing ⁰ due to the quantum confinement. In the low-temperature regime where ^kBT ⁰, the susceptibility as a function of Fermi energy rapidly changes between diamagnetism and paramagnetism in accordance with the discrete spectral structure due to the quantum confinement. In the high-temperature regime ^kBT⁰, the oscillatory structures due to the finite-size effect are all gone leaving a single diamagnetic peak in the bulk limit, regardless of atomic configuration of the graphene nanostructures. The diamagnetic current circulates entirely over the graphene nanostructures in the low-temperature regime, reflecting the absence of characteristic length scale in the massless Dirac system. As temperature increases, the current gradually becomes to circulate only near the edge, with the characteristic depth of ^λedge= v/2π^kBT.