# 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}
}
• 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…
2 Citations

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## References

SHOWING 1-10 OF 73 REFERENCES

• Physics
• 2012
We analyze the phase diagram of bilayer graphene (BLG) at zero temperature and zero doping. Assuming that at high energies the electronic system of BLG can be described within a weak-coupling theory
We study the Hubbard model on the AB-stacked bilayer honeycomb lattice with a repulsive onsite interaction U in second order perturbation theory and in self-consistent random phase approximation. We
• Physics
• 2021
Performing a leading-order renormalization group analysis, here we compute the effects of generic local or short-range electronic interactions in monolayer and Bernal bilayer graphene. Respectively
• Physics
• 2014
Electrons on the half-filled honeycomb lattice are expected to undergo a direct continuous transition from the semimetallic into the antiferromagnetic insulating phase with increase of on-site
• Physics
• 2017
We illuminate the intriguing role played by spatial anisotropy in three-dimensional Luttinger semimetals featuring quadratic band touching and long-range Coulomb interactions. We observe the
• Physics
• 2015
We construct and discuss the field theory for tensorial nematic order parameter coupled to gapless four-component fermions at the quadratic band touching point in three (spatial) dimensions. Within a
• Physics
Physical review letters
• 2016
Generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state.
• Physics
Physical review letters
• 2012
The Hubbard model on the Bernal-stacked honeycomb bilayer at half-filling is studied as a model system for bilayer graphene to find the antiferromagnetic ground state to be robust with respect to enhanced interlayer couplings and extended Coulomb interactions.
• Physics
• 2015
The metal-insulator transition has been a subject of intense research since Nevil Mott has first proposed that the metallic behavior of interacting electrons could turn to the insulating one as
• Physics
• 2012
We map out the possible ordered states in bilayer graphene at the neutrality point by extending the previous renormalization group treatment of many-body instabilities to finite temperature, trigonal