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

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.

18 pages, 5 figures, 1 table; v2: corrected typos and minor improvements, extended analysis of emergent Lorentz symmetry in four-fermion theory, published version

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Cited by in corpus (13)

• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Nematic Quantum Criticality in Dirac Systems
• Twist-tuned quantum criticality in moiré bilayer graphene
• Unconventional Gross-Neveu quantum criticality: Interaction-induced SO(3)-biadjoint insulator and emergent SU(3) symmetry
• Ubiquitous nematic Dirac semimetal emerging from interacting quadratic band touching system
• Quantum field theories of relativistic Luttinger fermions
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Quasiuniversality from all-in-all-out Weyl quantum criticality in pyrochlore iridates
• Spontaneous charge-ordered state in Bernal-stacked bilayer graphene
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Mean-field theory for self-interacting relativistic Luttinger fermions
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions