Energy gaps, magnetism, and electric field effects in bilayer graphene nanoribbons

TL;DR

This study uses first-principles calculations to explore how energy gaps and magnetism in bilayer graphene nanoribbons are affected by ribbon width, edge type, and external electric fields, revealing complex dependencies and sensitivities.

Contribution

It provides a detailed analysis of the interplay between electric fields, edge configurations, and magnetic properties in bilayer graphene nanoribbons using density functional theory.

Findings

Electric field increases gap in narrow ribbons, decreases in wide ribbons.

Armchair ribbons show three classes of gaps decreasing with width.

Magnetic properties vary with edge alignment and are sensitive to computational methods.

Abstract

Using a first principles density functional electronic structure method, we study the energy gaps and magnetism in bilayer graphene nanoribbons as a function of the ribbon width and the strength of an external electric field between the layers. We assume AB (Bernal) stacking and consider both armchair and zigzag edges and two edge alignments distinguished by a 60$^o$ rotation of one layer with respect to the other. Armchair ribbons exhibit three classes of bilayer gaps which decrease with increasing ribbon width. An external electric field between the layers increases the gap in narrow ribbons and decreases the gap for wide ribbons, a property which can be understood semi-analytically using a $\pi$-band tight-binding model and perturbation theory. The magnetic properties of zigzag edge ribbons are different for the two different edge alignments, and not robust for all exchange-correlation approximations considered. Bilayer ribbon gaps are sensitive to the presence or absence of magnetism.