Orbital Magnetism and Transport Phenomena in Two Dimensional Dirac Fermions in Weak Magnetic Field

We discuss the orbital magnetism and the Hall effect in the weak magnetic field in two dimensional Dirac fermion systems with energy gap. This model is related to the graphene sheet, organic conductors, and $d$-density wave superconductors. We found the strong diamagnetism and finite Hall conductivity even in gapped systems. We also discuss the relation between the weak-magnetic field formalism and the Landau quantization with the Euler-Maclaurin expansion.