Orbital magnetism and transport phenomena in two-dimensional Dirac fermions in a weak magnetic field

We discuss the orbital magnetism and the Hall effect in a weak magnetic field in two-dimensional Dirac fermion systems with an energy gap. This model is related to the graphene sheet, zero-gap organic conductors, and the $d$-density-wave state of cuprates. We found strong diamagnetism and anomalous Hall conductivity even in gapped systems. We also discuss the relation between results of the weak-magnetic-field formalism and those in a finite magnetic field with Landau quantization.

Figure 1

(Color) (a) Magnetic susceptibility $\overline{\chi }\equiv \chi 3{\pi }^2{c}^2\Gamma ∕e^2{v}^2$, (b) conductivity $\overline{\sigma }\equiv \sigma 2\pi h∕e^2$, and (c) Hall conductivity ${\overline{\sigma }}_{xy}\equiv {\sigma }_{xy}4{\pi }^{2}c{\Gamma }^2∕e^3{v}^{2}B$ of 2D Dirac fermions at zero temperature in a weak magnetic field, as functions of the scaled chemical potential $\mu ∕\Gamma$. The results (a) and (c) of the gapless case $(\Delta =0)$ are derived in Ref. 11.