Graphene has two atoms per unit cell with quasiparticles exhibiting Dirac-like behavior. These properties lead to interband in addition to intraband optical transitions and modify the $f$-sum rule on the longitudinal conductivity. The expected dependence of the corresponding spectral weight on the applied gate voltage $V_g$ in a field-effect graphene transistor is $\sim \mathrm{const}-{\mid V_g\mid }^{3∕2}$. For $V_g=0$, its temperature dependence is $T^3$ rather than the usual $T^2$. For the Hall conductivity, the corresponding spectral weight is determined by the Hall frequency ${\omega }_H$ which is linear in the carrier imbalance density $\rho$, and hence proportional to $V_g$, and is different from the cyclotron frequency for Dirac quasiparticles.

• Received 5 January 2007

DOI:https://doi.org/10.1103/PhysRevB.75.165407