Sum Rules for the Optical and Hall Conductivity in Graphene

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 ${\omega }_H$ 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.

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

References in corpus (5)

• Electric Field Effect in Atomically Thin Carbon Films
• Two Dimensional Atomic Crystals
• Magneto-optical conductivity in Graphene
• Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations II: transport properties
• Optical-conductivity sum rule in cuprates and unconventional charge density waves: a short review

Cited by in corpus (5)

• Valley Dependent Optoelectronics from Inversion Symmetry Breaking
• Non-linear electromagnetic response of graphene
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Transport in a Clean Graphene Sheet at Finite Temperature and Frequency
• Robustness of the optical-conductivity sum rule in Bilayer Graphene