Excitonic Instabilities and Insulating States in Bilayer Graphene

TL;DR

This paper investigates the various possible ground states of bilayer graphene using renormalization group techniques, revealing that most are insulating and identifying excitonic, magnetic, and density wave states as key contenders.

Contribution

It provides a comprehensive analysis of competing ordered states in bilayer graphene, highlighting excitonic instabilities and the likely insulating nature of its ground state.

Findings

Most ground states are insulating, except for superconductivity.

Multiple competing orders including ferromagnetism, superconductivity, and density waves.

Excitonic insulator states are strongly favored as the ground state.

Abstract

The competing ground states of bilayer graphene are studied by applying renormalization group techniques to a bilayer honeycomb lattice with nearest neighbor hopping. In the absence of interactions, the Fermi surface of this model at half-filling consists of two nodal points with momenta $\mathbf{K}$, $\mathbf{K}'$, where the conduction band and valence band touch each other, yielding a semi-metal. Since near these two points the energy dispersion is quadratic with perfect particle-hole symmetry, excitonic instabilities are inevitable if inter-band interactions are present. Using a perturbative renormalization group analysis up to the one-loop level, we find different competing ordered ground states, including ferromagnetism, superconductivity, spin and charge density wave states with ordering vector $\mathbf{Q}=\mathbf{K}-\mathbf{K}'$, and excitonic insulator states. In addition, two states with valley symmetry breaking are found in the excitonic insulating and ferromagnetic phases. This analysis strongly suggests that the ground state of bilayer graphene should be gapped, and with the exception of superconductivity, all other possible ground states are insulating.