Reexamination of the effective fine structure constant of graphene as measured in graphite

We present a refined and improved study of the influence of screening on the effective fine structure constant of graphene, alpha*, as measured in graphite using inelastic x-ray scattering. This followup to our previous study [J. P. Reed et al., Science 330, 805 (2010)] was carried out with two times better energy resolution, five times better momentum resolution, and an improved experimental setup with lower background. We compare our results to random-phase approximation (RPA) calculations and evaluate the relative importance of interlayer hopping, excitonic corrections, and screening from high energy excitations involving the sigma bands. We find that the static, limiting value of alpha* falls in the range 0.25-0.35, which is higher than our previous result of 0.14, but still below the value expected from RPA. We show the reduced value is not a consequence of interlayer hopping effects, which were ignored in our previous analysis, but of a combination of excitonic effects in the pi -> pi* particle-hole continuum, and background screening from the sigma-bonded electrons. We find that sigma-band screening is extremely strong at distances of less than a few nanometers, and should be highly effective at screening out short-distance, Hubbard-like interactions in graphene as well as other carbon allotropes.