Stacking Order dependent Electric Field tuning of the Band Gap in Graphene Multilayers

TL;DR

This study investigates how the stacking order of multilayer graphene influences the electric field-induced band gap, revealing significant dependence on stacking type and the impact of trigonal warping on the gap size.

Contribution

It demonstrates that stacking order critically affects the electric field tuning of the band gap in graphene multilayers, providing detailed predictions for different configurations.

Findings

ABC stacking yields a larger band gap than ABA in trilayer graphene.

The energy gap varies significantly with stacking in four-layer graphene.

Trigonal warping alters the induced electronic gap by about 30%.

Abstract

The effect of different stacking order of graphene multilayers on the electric field induced band gap is investigated. We considered a positively charged top and a negatively charged back gate in order to independently tune the band gap and the Fermi energy of three and four layer graphene systems. A tight-binding approach within a self-consistent Hartree approximation is used to calculate the induced charges on the different graphene layers. We found that the gap for trilayer graphene with the ABC stacking is much larger than the corresponding gap for the ABA trilayer. Also we predict that for four layers of graphene the energy gap strongly depends on the choice of stacking, and we found that the gap for the different types of stacking is much larger as compared to the case of Bernal stacking. Trigonal warping changes the size of the induced electronic gap by approximately 30% for intermediate and large values of the induced electron density.