Sum rules for the optical and Hall conductivity in graphene

2007/01/31 by V. P. Gusynin, S. G. Sharapov, J. P. Carbotte +1 · 1 citation
Materials Science · Physics and Astronomy · #Graphene research and applications #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.75.165407

published as Phys.Rev. B75 (2007) 165407 · 16 pages, RevTeX4, 4 EPS figures; v2: to match PRB version

arxiv created 2007/04/12 · openalex publication_date 2007/04/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Graphene has two atoms per unit cell with quasiparticles exhibiting 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 \ensuremath∼const\ensuremath-\ensuremath|V_g\ensuremath|^3∕2. For V_g=0, its temperature dependence is T³ rather than the usual T². For the Hall conductivity, the corresponding spectral weight is determined by the Hall frequency \ensuremathω_H which is linear in the carrier imbalance density \ensuremathρ, and hence proportional to V_g, and is different from the cyclotron frequency for Dirac quasiparticles.

Citations

• Transport of Dirac quasiparticles in graphene: Hall and optical conductivities
• Electric Field Effect in Atomically Thin Carbon Films
• Two-dimensional atomic crystals
• Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations. II. Transport properties

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• Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects