### 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) |
---|---|

Article number | 125439 |

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

Volume | 86 |

Issue number | 12 |

DOIs | |

State | Published - Sep 24 2012 |

### Fingerprint

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

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

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