Interaction-Induced Dirac Fermions from Quadratic Band Touching in Bilayer Graphene

Sumiran Pujari; Thomas C. Lang; Ganpathy Murthy; Ribhu K. Kaul

doi:10.1103/PhysRevLett.117.086404

Interaction-Induced Dirac Fermions from Quadratic Band Touching in Bilayer Graphene

Sumiran Pujari, Thomas C. Lang, Ganpathy Murthy, Ribhu K. Kaul

Research output: Contribution to journal › Article › peer-review

56 Scopus citations

Abstract

We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U/t despite the U=0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with (2+1)D Gross-Neveu criticality. We conclude that 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.

Original language	English
Article number	086404
Journal	Physical Review Letters
Volume	117
Issue number	8
DOIs	https://doi.org/10.1103/PhysRevLett.117.086404
State	Published - Aug 19 2016

Bibliographical note

Publisher Copyright:
© 2016 American Physical Society.

Funding

We thank F. Assaad, C.L. Kane, C. Honerkamp, A.C. Potter, O. Vafek, S. Wessel, A. Vishwanath, and K. Yang for useful discussions. We acknowledge NSF DMR-1056536 (S.P. and R.K.K.), NSF DMR-1306897 (G.M.), U.S.Israel BSF 2012120 (G.M.) for financial support, and NSF XSEDE DMR-150037, SuperMUC at Leibniz Supercomputing Centre and JURECA at JAlich Supercomputing Centre (JSC) for generous computer allocations.

Funders	Funder number
Leibniz Supercomputing Centre
JURECA
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	DMR-1056536, DMR-150037, 1056536, DMR-1306897, U.S.Israel BSF 2012120

ASJC Scopus subject areas

General Physics and Astronomy

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title = "Interaction-Induced Dirac Fermions from Quadratic Band Touching in Bilayer Graphene",

abstract = "We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U/t despite the U=0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with (2+1)D Gross-Neveu criticality. We conclude that 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.",

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N2 - We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U/t despite the U=0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with (2+1)D Gross-Neveu criticality. We conclude that 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.

AB - We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U/t despite the U=0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with (2+1)D Gross-Neveu criticality. We conclude that 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.

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Interaction-Induced Dirac Fermions from Quadratic Band Touching in Bilayer Graphene

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

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