Coexistence and competition of nematic and gapped states in bilayer graphene

E. V. Gorbar, V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy
Phys. Rev. B 86, 125439 – Published 24 September 2012

Abstract

In bilayer graphene, the phase diagram in the plane of a strain-induced bare nematic term N0 and a top-bottom gates voltage imbalance U0 is obtained by solving the gap equation in the random-phase approximation. At nonzero N0 and U0, 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 N0, respectively. The existence of a critical end point where the line of first-order phase transitions terminates is predicted. For N0=0, a pure gapped state with a broken spin-valley symmetry is the ground state of the system. As N0 increases, the nematic order parameter increases, and the gap weakens in the hybrid state. For U0=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 U0 suppresses the critical value of the strain. The relevance of these results to recent experiments is briefly discussed.

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  • Received 18 April 2012

DOI:https://doi.org/10.1103/PhysRevB.86.125439

©2012 American Physical Society

Authors & Affiliations

E. V. Gorbar1,2, V. P. Gusynin2, V. A. Miransky3, and I. A. Shovkovy4

  • 1Department of Physics, Taras Shevchenko National Kiev University, Kiev 03022, Ukraine
  • 2Bogolyubov Institute for Theoretical Physics, Kiev 03680, Ukraine
  • 3Department of Applied Mathematics, Western University, London, Ontario, Canada, N6A 5B7
  • 4Department of Applied Sciences and Mathematics, Arizona State University, Mesa, Arizona 85212, USA

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Issue

Vol. 86, Iss. 12 — 15 September 2012

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