Sum Rules for the Optical and Hall Conductivity in Graphene

Details Sum Rules for the Optical and Hall Conductivity in Graphene Sum Rules for the Optical and Hall Conductivity in Graphene

2007-01-03

arxiv.org/abs/cond-mat/0701053v2

Phys.Rev. B75 (2007) 165407

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

16 pages, RevTeX4, 4 EPS figures; v2: to match PRB version

Scientific paper

10.1103/PhysRevB.75.165407

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 $\omega_H$ 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.

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