Calibration of the fine-structure constant of graphene by time-dependent density-functional theory

One of the amazing properties of graphene is the ultrarelativistic behavior of its loosely bound electrons, mimicking massless fermions that move with a constant velocity, inversely proportional to a fine-structure constant α g of the order of unity. The effective interaction between these quasiparticles is, however, better controlled by the coupling parameter α ∗ g = α g / ε , which accounts for the dynamic screening due to the complex permittivity ε of the many-valence electron system. This concept was introduced in a couple of previous studies [Reed et al., Science 330, 805 (2010) and Gan et al., Phys. Rev. B 93, 195150 (2016)], where inelastic x-ray scattering measurements on crystal graphite were converted into an experimentally derived form of α ∗ g for graphene, over an energy-momentum region on the eV Å − 1 scale. Here, an accurate theoretical framework is provided for α ∗ g , using time-dependent density-functional theory in the random-phase approximation, with a cutoff in the interaction between excited electrons in graphene, which translates to an effective interlayer interaction in graphite. The predictions of the approach are in excellent agreement with the above-mentioned measurements, suggesting a calibration method to substantially improve the experimental derivation of α ∗ g , which tends to a static limiting value of ∼ 0.14 . Thus, the ab initio calibration procedure outlined demonstrates the accuracy of perturbation expansion treatments for the two-dimensional gas of massless Dirac fermions in graphene, in parallel with quantum electrodynamics.