Graphene Nano-Ribbons: Major differences in the fundamental gap as its length is increased either in the zig-zag or the armchair directions

TL;DR

This paper investigates how the electronic gap of graphene nano-ribbons varies with size along different crystallographic directions, revealing oscillations and smooth changes linked to edge-localized charges and magnetic moments.

Contribution

It provides a detailed analysis of the gap variation in GNRs with respect to their length in zig-zag and armchair directions, highlighting the impact of edge states.

Findings

Gap varies smoothly with fixed n, oscillates with fixed m.

Edge-localized charges and magnetic moments influence gap behavior.

Oscillations pose challenges for electronic applications.

Abstract

Controlling the forbidden gap of graphene nano-ribbons (GNR) is a major challenge that has to be attained if this attractive material has to be used in micro- and nano-electronics. Using an unambiguous notation {m,n}-GNR, where m (n) is the number of six carbon rings in the arm-chair (zig-zag) directions, we investigate how varies the HOMO-LUMO gap when the size of the GNR is varied by increasing either m or n, while keeping the other variable fixed. It is shown that no matter whether charge- or spin-density-waves solutions are considered, the gap varies smoothly when n is kept fixed whereas it oscillates when the opposite is done, posing serious difficulties to the control of the gap. It is argued that the origin of this behavior is the fact that excess or defect charges or magnetic moments are mostly localized at zig-zag edges.