Sum Rules for the Optical and Hall Conductivity in Graphene

Gusynin, V. P.; Sharapov, S. G.; Carbotte, J. P.

Sum Rules for the Optical and Hall Conductivity in Graphene

Authors

Gusynin, V. P.

Sharapov, S. G.

Carbotte, J. P.

Description

Graphene has two atoms per unit cell with quasiparticles exhibiting the 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 $\sim {const}- |V_g|^{3/2}$. 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 $ω_H$ which is linear in the carrier imbalance density $ρ$, and hence proportional to $V_g$, and is different from the cyclotron frequency for Dirac quasiparticles.
16 pages, RevTeX4, 4 EPS figures; v2: to match PRB version