1204.2286 (E. V. Gorbar et al.)

Coexistence and competition of nematic and gapped states in bilayer
graphene    [PDF]

E. V. Gorbar, V. P. Gusynin, V. A. Miransky, I. A. Shovkovy

A coupled set of gap equations for the nematic and several types of gapped order parameters in bilayer graphene is analyzed. The phase diagram in the plane of a strain induced bare nematic term, ${\cal N}_{0}$, and a top-bottom gates voltage imbalance, $U_{0}$, is obtained. For ${\cal N}_0=0$, a symmetry broken gapped state has the lowest energy. We show that for nonzero and sufficiently small ${\cal N}_{0}$, a hybrid state with gapped and nematic order parameters is the ground state of the system. As ${\cal N}_{0}$ increases, the nematic order parameter increases and the gap weakens in the hybrid state. Finally, when the strain reaches a critical value, a quantum second order phase transition into a gapless nematic state occurs. A small nonzero top-bottom gates voltage imbalance suppresses the critical value of the strain. At large values of $U_{0}$, a first order phase transition between the two types of gapped states is found. The existence of a critical end point in the phase diagram is predicted.

View original: http://arxiv.org/abs/1204.2286