Critical Behavior in Graphene with Coulomb Interactions

TL;DR

This paper shows that Coulomb interactions cause electrons in graphene to exhibit critical behavior with power law correlations, leading to unique instabilities and measurable effects linked to classical 2D systems.

Contribution

It reveals how Coulomb interactions induce critical power law behavior and instabilities in graphene's electron correlations, a novel insight into its many-body physics.

Findings

Electrons in graphene exhibit interaction-dependent power law correlations.

Increasing Coulomb strength leads to a transition from real to complex power law exponents.

The study connects graphene's behavior to classical two-dimensional systems.

Abstract

We demonstrate that in the presence of Coulomb interactions, electrons in graphene behave like a critical system, supporting power law correlations with interaction-dependent exponents. An asymptotic analysis shows that the origin of this behavior lies in particle-hole scattering, for which the Coulomb interaction induces anomalously close approaches. With increasing interaction strength the relevant power law changes from real to complex, leading to an unusual instability characterized by a complex-valued susceptibility in the thermodynamic limit. Measurable quantities, as well as the connection to classical two dimensional systems, are discussed.