The electron many-body problem in graphene

TL;DR

This paper reviews the current understanding of electron-electron interactions in graphene, emphasizing its scale-dependent dielectric properties and proposing a framework to reconcile experimental differences in observed interaction effects.

Contribution

It introduces a scale-dependent effective fine structure constant for graphene and offers a method to unify diverse experimental results on electron interactions.

Findings

Graphene's dielectric properties influence electron interactions significantly.

The effective fine structure constant varies from about 1/7 in static to 2.6 in optical regimes.

Coulomb interaction strength in graphene depends on the scale of the phenomenon.

Abstract

We give a brief summary of the current status of the electron many-body problem in graphene. We claim that graphene has intrinsic dielectric properties which should dress the interactions among the quasiparticles, and may explain why the observation of electron-electron renormalization effects has been so elusive in the recent experiments. We argue that the strength of Coulomb interactions in graphene may be characterized by an effective fine structure constant given by $\alpha^{\star}(\mathbf{k},\omega)\equiv2.2/\epsilon(\mathbf{k},\omega)$, where $\epsilon(\mathbf{k},\omega)$ is the dynamical dielectric function. At long wavelengths, $\alpha^{\star}(\mathbf{k},\omega)$ appears to have its smallest value in the static regime, where $\alpha^{\star}(\mathbf{k}\to0,0)\approx1/7$ according to recent inelastic x-ray measurements, and the largest value in the optical limit, where $\alpha^{\star}(0,\omega)\approx2.6$. We conclude that the strength of Coulomb interactions in graphene is not universal, but depends highly on the scale of the phenomenon of interest. We propose a prescription in order to reconcile different experiments.