Density functional theory calculations of the electric-field-induced Dirac cones and quantum valley Hall state in ABA-stacked trilayer graphene

We have investigated ABA-stacked trilayer graphene under a perpendicular electric field by using the density functional theory (DFT) calculations, which may contribute to the resolution of the discrepancies between experimental and theoretical results on the electric-field-induced band gap and topological phase transition. We found that the electric field opens a band gap at a low field and closes the gap at a high field, supporting one of the experimental results. While the seven electric-field-induced Dirac cones with mass gaps predicted in recent tight-binding (TB) models are confirmed, our DFT calculations demonstrate a phase transition from a quantum valley Hall insulator to a semimetal, contrasting to the TB model prediction of a topological phase transition between topologically nontrivial insulators at a high electric field.