• DOI:10.1103/PhysRevB.104.045101
• Corpus ID: 233407651

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

@article{Ray2021GrossNeveuHeisenbergCF,
  title={Gross-Neveu-Heisenberg criticality from competing nematic and antiferromagnetic orders in bilayer graphene},
  author={Shouryya Ray and Lukas Janssen},
  journal={Physical Review B},
  year={2021}
}

• Shouryya Ray, L. Janssen
• Published 26 April 2021
• Physics
• Physical Review B

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 the continuous spatial rotational symmetry on the honeycomb bilayer. Implications for experiments in bilayer graphene are discussed.