Six-band nearest-neighbor tight-binding model for the $\pi $-bands of bulk graphene and graphene nanoribbons*

The commonly used single-p$_{z}$ orbital first nearest-neighbor tight-binding model faces two main problems: (i) it fails to reproduce asymmetries in the bulk graphene bands; (ii) it cannot provide a realistic model for hydrogen passivation of the edge atoms. As a result, some armchair graphene nanoribbons (AGNRs) are incorrectly predicted as metallic. A new nearest-neighbor, three orbital per atom p/d tight-binding model [1] is built to address these issues. The parameters of the model are fit to bandstructures obtained from first-principles density-functional theory and many-body perturbation theory within the GW approximation, giving excellent agreement with the ab initio AGNR bands. This model is employed to calculate the current-voltage characteristics of an AGNR MOSFET and the conductance of rough-edge AGNRs, finding significant differences versus the single-p$_{z}$ model. Taken together these results demonstrate the importance of an accurate and computational efficient band structure model for predicting the performance of graphene-based nanodevices. [1] T. B. Boykin, M. Luisier, G. Klimeck, X. Jiang, N. Kharche, Y. Zhou and S. Nayak, J. Appl. Phys. 109, 104304 (2011)