Orbital magnetism of graphene nanostructures

•Orbital diamagnetism is studied for graphene ribbons and graphene flakes.•The orbital susceptibility and distribution of the diamagnetic current are calculated.•The dependence on the edge configuration and the global shape is argued.

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 kBTkBT to the characteristic level spacing ɛ0ɛ0 due to the quantum confinement. In the low-temperature regime where kBT⪯¡ɛ0kBT⪯¡ɛ0, 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 kBT⪢ɛ0kBT⪢ɛ0, 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=ℏv/2πkBTλedge=ℏv/2πkBT.