Effects of magnetism and electric field on the energy gap of bilayer graphene nanoflakes

TL;DR

This study investigates how magnetism and external electric fields influence the energy gap of bilayer graphene nanoflakes, revealing the roles of edge type, width, length, and magnetic effects on electronic properties.

Contribution

It provides a detailed first-principles analysis of the combined effects of magnetism and electric fields on bilayer graphene nanoflakes, considering various edge alignments and geometries.

Findings

Energy gaps decrease with electric field strength, but no critical gap threshold is predicted.

Magnetism significantly enhances energy gaps due to geometrical confinement.

Armchair nanoflakes lack metallic behavior seen in nanoribbons.

Abstract

We study the effect of magnetism and perpendicular external electric field strengths on the energy gap of length confined bilayer graphene nanoribbons (or nanoflakes) as a function of ribbon width and length using a \textit{first principles} density functional electronic structure method and a semi-local exchange-correlation approximation. We assume AB (Bernal) bilayer stacking and consider both armchair and zigzag edges, and for each edge type, we consider the two edge alignments, namely, $\alpha$ and $\beta$ edge alignment. For the armchair nanoflakes we identify three distinct classes of bilayer energy gaps, determined by the number of carbon chains in the width direction ({\it N} = 3{\it p}, 3{\it p}+1 and 3{\it p}+2, {\it p} is an integer), and the gaps decrease with increasing width except for class 3{\it p}+2 armchair nanoribbons. Metallic-like behavior seen in armchair bilayer nanoribbons are found to be absent in armchair nanoflakes. Class 3{\it p}+2 armchair nanoflakes show significant length dependence. We find that the gaps decrease with the applied electric fields due to large intrinsic gap of the nanoflake. The existence of a critical gap with respect to the applied field, therefore, is not predicted by our calculations. Magnetism between the layers plays a major role in enhancing the gap values resulting from the geometrical confinement, hinting at an interplay of magnetism and geometrical confinement in finite size bilayer graphene.