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Sum Rules for the Optical and Hall Conductivity in Graphene

V. P. Gusynin·S. G. Sharapov·J. P. Carbotte
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Abstract

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.

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V. P. Gusynin, S. G. Sharapov, J. P. Carbotte. 2007-04-12. Sum Rules for the Optical and Hall Conductivity in Graphene. https://doi.org/10.1103/physrevb.75.165407

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