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Sum rules for the optical and Hall conductivity in graphene

2007; American Physical Society; Volume: 75; Issue: 16 Linguagem: Inglês

10.1103/physrevb.75.165407

1550-235X

V. P. Gusynin, S. G. Sharapov, J. P. Ćarbotte,

Topological Materials and Phenomena

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.