Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2011-11-08
Physics
Condensed Matter
Strongly Correlated Electrons
25 pages, 6 figures
Scientific paper
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[1,2] there is a single gate while in others[3,4], 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. For spin-1/2 fermions, 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 Refs.[5] and [6]. 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[5,6]. Our results can help reconcile the recent results of two seemingly contradictory experiments[2,4]. We also consider the effects of an applied magnetic field on the system in the antiferromagnetic phase via variational mean field theory, obtaining results in qualitative agreement with the experimental data. We find that the antiferromagnetic order parameter increases with field, at first quadratically at low fields, then as B/ln(B/B_0) at higher fields. Similar analysis is presented for spinless fermions.
Throckmorton Robert E.
Vafek Oskar
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