The Effects of the Mean-Field Interaction on the Anderson Localization of Graphene Nanoribbons

A generalized tight-binding (TB) model,\footnote{Hancock {\em et al.} PRB {\textbf 81}, 245402 (2010).} which includes a mean-field Hubbard-{\em U} and up to 3rd nearest-neighbor hopping terms, is applied to edge-disordered zigzag graphene nanoribbons in order to study spin-transport within the Landauer-B\"utticker formalism. Edge-disorder is modeled by random perturbation of the on-site energy in the range $-E..E$ on all edge atoms, and the resulting Anderson localization lengths determined. We compared the Anderson localization lengths and spin-transport features obtained from the generalized model, an extended TB model (non-interacting) and the simplified TB model (1st nearest neighbor hopping only). Within the range $\pm E=$0.5~eV the Anderson localization length for a single spin was found to decrease by 86.4\% with the introduction of the Hubbard-$U$ in the generalized model compared to the non-interacting models, whereas the opposite spin remained unchanged across all model types. For the range $\pm E=$2.0~eV the Anderson localization length for both spin types decreased by 71.4\% and 76.2\% in the generalized model when compared to the extended TB model, and 76.5\% and 80.4\% when compared to the simplified TB model.