Sum rules for the optical and Hall conductivity in graphene

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 similar to const-vertical bar V-g vertical bar(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.