Gate-induced Dirac cones in multilayer graphenes

TL;DR

This paper investigates how perpendicular electric fields induce tunable Dirac cones in multilayer graphenes, revealing emergent topological states and valley Hall effects depending on layer number and symmetry.

Contribution

It demonstrates the emergence of gate-induced Dirac cones and valley Hall states in multilayer graphenes, highlighting the role of symmetry and electric field tuning.

Findings

Electric fields create tunable Dirac cones in multilayer graphene.

Valley Hall states appear in odd-layer graphenes with chiral symmetry.

Edge modes fill the gap in ABA trilayer graphene under electric field.

Abstract

We study the electronic structures of ABA (Bernal) stacked multilayer graphenes in uniform perpendicular electric field, and show that the interplay of the trigonal warping and the potential asymmetry gives rise to a number of emergent Dirac cones nearly touching at zero energy. The band velocity and the energy region (typically a few tens of meV) of these gate-induced Dirac cones are tunable with the external electric field. In ABA trilayer graphene, in particular, applying an electric field induces a non-trivial valley Hall state, where the energy gap at the Dirac point is filled by chiral edge modes which propagate in opposite directions between two valleys. In four-layer graphene, in contrast, the valley Hall conductivity is zero and there are no edge modes filling in the gap. A nontrivial valley Hall state generally occurs in asymmetric odd layer graphenes and this is closely related to a hidden chiral symmetry which exists only in odd layer graphenes.