Electron-Electron Interactions in Graphene: Current Status and Perspectives

The problem of electron-electron interactions in graphene is reviewed. Starting from the screening of long-range interactions in these systems, the existence of an emerging Dirac liquid of Lorentz invariant quasiparticles in the weak-coupling regime is discussed, as well as the formation of strongly correlated electronic states in the strong-coupling regime. The analogy and connections between the many-body problem and the Coulomb impurity problem are also analyzed. The problem of the magnetic instability and Kondo effect of impurities and/or adatoms in graphene is also discussed in analogy with classical models of many-body effects in ordinary metals. Lorentz invariance is shown to play a fundamental role and…