Measurement of the Optical Conductivity of Graphene

Abstract

Optical reflectivity and transmission measurements over photon energies between 0.2 and 1.2 eV were performed on single-crystal graphene samples on a transparent SiO2 substrate. For photon energies above 0.5 eV, graphene yielded a spectrally flat optical absorbance of (2.3 +/- 0.2)%. This result is in agreement with a constant absorbance of pi*alpha, or a sheet conductivity of pi*e^2/2h, predicted within a model of non-interacting massless Dirac Fermions. This simple result breaks down at lower photon energies, where both spectral and sample-to-sample variations were observed. This "non-universal" behavior is explained by including the effects of doping and finite temperature, as well as contributions from intraband transitions.

9 pages, 4 figures, Phys. Rev. Lett. 101, 196405 (2008)

References in corpus (13)

• Electric Field Effect in Atomically Thin Carbon Films
• The Raman Fingerprint of Graphene
• Universal Dynamic Conductivity and Quantized Visible Opacity of Suspended Graphene
• Measurement of Scattering Rate and Minimum Conductivity in Graphene
• Universal dynamical conductance in graphite
• Optical far-infrared properties of graphene monolayer and multilayers
• The optical conductivity of graphene in the visible region of the spectrum
• Unusual Microwave Response of Dirac Quasiparticles in Graphene
• Optical and magneto-optical far-infrared properties of bilayer graphene
• Magneto-optical properties of multilayer graphenes
• Effect of electron-electron interactions on the conductivity of clean graphene
• Landauer conductance and twisted boundary conditions for Dirac fermions in two space dimensions
• Transport equations for a two-dimensional electron gas with spin-orbit interaction

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