Splitting of the zero-energy edge states in bilayer graphene

Abstract

Bilayer graphene nanoribbons with zigzag termination are studied within the tight-binding model. We also include single-site electron-electron interactions via the Hubbard model within the unrestricted Hartree-Fock approach. We show that either the interactions between the outermost edge atoms or the presence of a magnetic order can cause a splitting of the zero-energy edge states. Two kinds of edge alignments are considered. For one kind of edge alignment $(\ensuremath{\alpha})$ the system is nonmagnetic unless the Hubbard parameter $U$ becomes greater than a critical value ${U}_{c}$. For the other kind of edge alignment $(\ensuremath{\beta})$ the system is magnetic for any $Ug0$. Our results agree very well with ab initio density functional theory calculations.