Electron-electron interactions in graphene bilayers

TL;DR

This paper investigates electron-electron interactions in graphene bilayers, revealing that they can induce a strong-coupling broken symmetry state with an energy gap, akin to one-dimensional systems, despite being two-dimensional.

Contribution

It demonstrates through perturbative RG analysis that neutral graphene bilayers can develop a layer-pseudospin ferromagnetic state due to electron interactions.

Findings

Interactions can induce a gapped, ferromagnetic phase.

Graphene bilayers behave like 1D systems in certain interaction regimes.

Strong-coupling broken symmetry state is theoretically predicted.

Abstract

Electrons most often organize into Fermi-liquid states in which electron-electron interactions play an inessential role. A well known exception is the case of one-dimensional (1D) electron systems (1DES). In 1D the electron Fermi-surface consists of points, and divergences associated with low-energy particle-hole excitations abound when electron-electron interactions are described perturbatively. In higher space dimensions, the corresponding divergences occur only when Fermi lines or surfaces satisfy idealized nesting conditions. In this article we discuss electron-electron interactions in 2D graphene bilayer systems which behave in many ways as if they were one-dimensional, because they have Fermi points instead of Fermi lines and because their particle-hole energies have a quadratic dispersion which compensates for the difference between 1D and 2D phase space. We conclude, on the basis of a perturbative RG calculation similar to that commonly employed in 1D systems, that interactions in neutral graphene bilayers can drive the system into a strong-coupling broken symmetry state with layer-pseudospin ferromagnetism and an energy gap.