Coexistence and competition of nematic and gapped states in bilayer graphene

Details Coexistence and competition of nematic and gapped states in bilayer graphene Coexistence and competition of nematic and gapped states in bilayer graphene

2012-04-10

arxiv.org/abs/1204.2286v1

Physics

Condensed Matter

Strongly Correlated Electrons

5 pages, 3 figures

Scientific paper

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.

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