### Abstract

In bilayer graphene, the phase diagram in the plane of a strain-induced bare nematic term N _{0} and a top-bottom gates voltage imbalance U _{0} is obtained by solving the gap equation in the random-phase approximation. At nonzero N _{0} and U _{0}, the phase diagram consists of two hybrid spin-valley symmetry-broken phases with both nontrivial nematic and mass-type order parameters. The corresponding phases are separated by a critical line of first- and second-order phase transitions at small and large values of N _{0}, respectively. The existence of a critical end point where the line of first-order phase transitions terminates is predicted. For N _{0}=0, a pure gapped state with a broken spin-valley symmetry is the ground state of the system. As N _{0} increases, the nematic order parameter increases, and the gap weakens in the hybrid state. For U _{0}=0, a quantum second-order phase transition from the hybrid state into a pure gapless nematic state occurs when the strain reaches a critical value. A nonzero U _{0} suppresses the critical value of the strain. The relevance of these results to recent experiments is briefly discussed.

Original language | English (US) |
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Article number | 125439 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 86 |

Issue number | 12 |

DOIs | |

State | Published - Sep 24 2012 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*86*(12), [125439]. https://doi.org/10.1103/PhysRevB.86.125439

**Coexistence and competition of nematic and gapped states in bilayer graphene.** / Gorbar, E. V.; Gusynin, V. P.; Miransky, V. A.; Shovkovy, Igor.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 86, no. 12, 125439. https://doi.org/10.1103/PhysRevB.86.125439

}

TY - JOUR

T1 - Coexistence and competition of nematic and gapped states in bilayer graphene

AU - Gorbar, E. V.

AU - Gusynin, V. P.

AU - Miransky, V. A.

AU - Shovkovy, Igor

PY - 2012/9/24

Y1 - 2012/9/24

N2 - In bilayer graphene, the phase diagram in the plane of a strain-induced bare nematic term N 0 and a top-bottom gates voltage imbalance U 0 is obtained by solving the gap equation in the random-phase approximation. At nonzero N 0 and U 0, the phase diagram consists of two hybrid spin-valley symmetry-broken phases with both nontrivial nematic and mass-type order parameters. The corresponding phases are separated by a critical line of first- and second-order phase transitions at small and large values of N 0, respectively. The existence of a critical end point where the line of first-order phase transitions terminates is predicted. For N 0=0, a pure gapped state with a broken spin-valley symmetry is the ground state of the system. As N 0 increases, the nematic order parameter increases, and the gap weakens in the hybrid state. For U 0=0, a quantum second-order phase transition from the hybrid state into a pure gapless nematic state occurs when the strain reaches a critical value. A nonzero U 0 suppresses the critical value of the strain. The relevance of these results to recent experiments is briefly discussed.

AB - In bilayer graphene, the phase diagram in the plane of a strain-induced bare nematic term N 0 and a top-bottom gates voltage imbalance U 0 is obtained by solving the gap equation in the random-phase approximation. At nonzero N 0 and U 0, the phase diagram consists of two hybrid spin-valley symmetry-broken phases with both nontrivial nematic and mass-type order parameters. The corresponding phases are separated by a critical line of first- and second-order phase transitions at small and large values of N 0, respectively. The existence of a critical end point where the line of first-order phase transitions terminates is predicted. For N 0=0, a pure gapped state with a broken spin-valley symmetry is the ground state of the system. As N 0 increases, the nematic order parameter increases, and the gap weakens in the hybrid state. For U 0=0, a quantum second-order phase transition from the hybrid state into a pure gapless nematic state occurs when the strain reaches a critical value. A nonzero U 0 suppresses the critical value of the strain. The relevance of these results to recent experiments is briefly discussed.

UR - http://www.scopus.com/inward/record.url?scp=84866978823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866978823&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.86.125439

DO - 10.1103/PhysRevB.86.125439

M3 - Article

VL - 86

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 12

M1 - 125439

ER -