Gross-Neveu-Heisenberg criticality from competing nematic and antiferromagnetic orders in bilayer graphene

TL;DR

This paper investigates the quantum phase transitions in bilayer graphene, revealing a continuous nematic to coexistent phase transition with emergent Lorentz symmetry and a weakly first-order transition to antiferromagnetic order.

Contribution

It demonstrates the universality class of the nematic to coexistent transition and characterizes the nature of the coexistence-to-antiferromagnetic transition in bilayer graphene.

Findings

Nematic and antiferromagnetic orders can coexist in bilayer graphene.

The nematic to coexistence transition is continuous with emergent Lorentz symmetry.

The transition to antiferromagnetic order is weakly first order.

Abstract

We study the phase diagram of an effective model of competing nematic and antiferromagnetic orders of interacting electrons on the Bernal-stacked honeycomb bilayer, as relevant for bilayer graphene. In the noninteracting limit, the model features a semimetallic ground state with quadratic band touching points at the Fermi level. Taking the effects of short-range interactions into account, we demonstrate the existence of an extended region in the mean-field phase diagram characterized by coexisting nematic and antiferromagnetic orders. By means of a renormalization group approach, we reveal that the quantum phase transition from nematic to coexistent nematic-antiferromagnetic orders is continuous and characterized by emergent Lorentz symmetry. It falls into the $(2+1)$-dimensional relativistic Gross-Neveu-Heisenberg quantum universality class, which has recently been much investigated in the context of interacting Dirac systems in two spatial dimensions. The coexistence-to-antiferromagnetic transition, by contrast, turns out to be weakly first order as a consequence of the absence of continuous spatial rotational symmetry on the honeycomb bilayer. Implications for experiments in bilayer graphene are discussed.