Electron-Electron Interactions in Graphene: Current Status and Perspectives

TL;DR

This review discusses the current understanding of electron-electron interactions in graphene, highlighting the emergence of Lorentz-invariant quasiparticles, correlated states, and many-body effects, while identifying open questions for future research.

Contribution

It provides a comprehensive overview of electron-electron interactions in graphene, emphasizing the role of Lorentz invariance and connecting various many-body phenomena.

Findings

Existence of a Dirac liquid with Lorentz invariance in weak coupling

Strongly correlated electronic states in strong coupling regime

Connections between many-body effects and Coulomb impurity problem

Abstract

We review the problem of electron-electron interactions in graphene. Starting from the screening of long range interactions in these systems, we discuss the existence of an emerging Dirac liquid of Lorentz invariant quasi-particles in the weak coupling regime, and strongly correlated electronic states in the strong coupling regime. We also analyze the analogy and connections between the many-body problem and the Coulomb impurity problem. 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. We show that Lorentz invariance plays a fundamental role and leads to effects that span the whole spectrum, from the ultraviolet to the infrared. The effect of an emerging Lorentz invariance is also discussed in the context of finite size and edge effects as well as mesoscopic physics. We also briefly discuss the effects of strong magnetic fields in single layers and review some of the main aspects of the many-body problem in graphene bilayers. In addition to reviewing the fully understood aspects of the many-body problem in graphene, we show that a plethora of interesting issues remain open, both theoretically and experimentally, and that the field of graphene research is still exciting and vibrant.