Measurement of the Optical Conductivity of Graphene

Measurement of the Optical Conductivity of Graphene

| Kin Fai Mak, Matthew Y. Sfeir, Yang Wu, Chun Hung Lui, James A. Misewich and Tony F. Heinz
The optical conductivity of single-layer graphene was measured over the photon energy range of 0.2–1.2 eV. The results showed a spectrally flat optical absorbance of (2.3 ± 0.2)%, consistent with the theoretical prediction of πα = 2.293% for massless Dirac Fermions. This universal behavior holds for photon energies above 0.5 eV, but breaks down at lower energies due to factors like doping and finite temperature. The absorbance was measured using optical transmission and reflection techniques on large-area, single-crystal graphene samples on a SiO₂ substrate. The results were consistent across different samples, showing robust optical conductivity. However, at lower photon energies, significant spectral variations were observed, indicating non-universal behavior. The universal optical conductivity is considered the high-frequency counterpart of the minimal dc conductivity of graphene. The study also identified limitations imposed by finite temperature and doping. The optical conductivity was calculated using the Kubo formula, considering both inter- and intraband contributions. The results were consistent with theoretical predictions, and the experimental data showed a slight increase in absorbance with photon energy, possibly due to many-body effects and spectral broadening. The study highlights the importance of considering doping and temperature effects in the interpretation of optical conductivity measurements in graphene.The optical conductivity of single-layer graphene was measured over the photon energy range of 0.2–1.2 eV. The results showed a spectrally flat optical absorbance of (2.3 ± 0.2)%, consistent with the theoretical prediction of πα = 2.293% for massless Dirac Fermions. This universal behavior holds for photon energies above 0.5 eV, but breaks down at lower energies due to factors like doping and finite temperature. The absorbance was measured using optical transmission and reflection techniques on large-area, single-crystal graphene samples on a SiO₂ substrate. The results were consistent across different samples, showing robust optical conductivity. However, at lower photon energies, significant spectral variations were observed, indicating non-universal behavior. The universal optical conductivity is considered the high-frequency counterpart of the minimal dc conductivity of graphene. The study also identified limitations imposed by finite temperature and doping. The optical conductivity was calculated using the Kubo formula, considering both inter- and intraband contributions. The results were consistent with theoretical predictions, and the experimental data showed a slight increase in absorbance with photon energy, possibly due to many-body effects and spectral broadening. The study highlights the importance of considering doping and temperature effects in the interpretation of optical conductivity measurements in graphene.
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Understanding Measurement of the optical conductivity of graphene.