Orbital diamagnetism of weakly doped bilayer graphene in a magnetic field

We investigate the orbital diamagnetism of weakly doped bilayer graphene (BLG) in a spatially smoothly varying magnetic field and obtain the general analytic expression for the orbital susceptibility of BLG, with finite wavenumber and Fermi energy, at zero temperature. We find that the magnetic field screening factor of BLG is dependent on the wavenumber, which results in a more complicated screening behavior compared with that of monolayer graphene (MLG). We also study the induced magnetization and electric current in BLG, under a nonuniform magnetic field, and find that they are qualitatively different from those for MLG and the two-dimensional electron gas (2DEG). However, as for MLG, a magnetic object placed above BLG is repelled by a diamagnetic force from the BLG, which is approximately equivalent to the force produced by its mirror image on the other side of the BLG with a reduced amplitude dependent on the typical length of the systems. BLG shows crossover behaviors in the responses to the external magnetic field, intermediate between those of MLG and 2DEG.