Fermions on bilayer graphene: symmetry breaking for B=0 and nu=0

TL;DR

This paper investigates how finite-range interactions influence symmetry-breaking phases in bilayer graphene, revealing a transition from antiferromagnetic to nematic phases and analyzing magnetic field effects on these phases.

Contribution

It extends previous RG analyses to finite-range interactions and maps out the resulting phase diagram, including effects of magnetic fields on symmetry-breaking phases.

Findings

Short-range interactions favor antiferromagnetic phase with a spectral gap.

Long-range interactions favor a gapless nematic phase with split Dirac cones.

Magnetic fields modify the antiferromagnetic order parameter and energy gap, with specific dependencies.

Abstract

We extend previous analyses of fermions on a honeycomb bilayer lattice via weak-coupling renormalization group (RG) methods with extremely short-range and extremely long-range interactions to the case of finite-range interactions. In particular, we consider different types of interactions including screened Coulomb interactions, much like those produced by a point charge placed either above a single infinite conducting plate or exactly halfway between two parallel infinite conducting plates. Our considerations are motivated by the fact that, in some recent experiments on bilayer graphene there is a single gate while in others there are two gates, which can function as the conducting planes and which, we argue, can lead to distinct broken symmetry phases. We map out the phases that the system enters as a function of the range of the interaction. We discover that the system enters an antiferromagnetic phase for short ranges of the interaction and a nematic phase at long ranges, in agreement with previous work. While the antiferromagnetic phase results in a gap in the spectrum, the nematic phase is gapless, splitting the quadratic degeneracy points into two Dirac cones each. We also consider the effects of an applied magnetic field on the system in the antiferromagnetic phase via variational mean field theory. At low fields, we find that the antiferromagnetic order parameter, Delta(B)-Delta(0) \sim B^2. At higher fields, when omega_c > 2*Delta_0, we find that Delta(B)=omega_c/[ln(omega_c/Delta(0))+C], where C=0.67 and omega_c=eB/m^*c. We also determine the energy gap for creating electron-hole excitations in the system, and, at high fields, we find it to be a*omega_c+2*Delta(B), where a is a non-universal, interaction-dependent, constant.