Edge-Corrected Mean-Field Hubbard Model: Principle and Applications in 2D Materials

This work reviews the current progress of tight-binding methods and the recent edge-modified mean-field Hubbard model. Undercoordinated atoms (atoms not fully coordinated) exist at a high rate in nanomaterials with their impact overlooked. A quantum theory was proposed to calculate electronic structure of nanomaterials by incorporating bond order-length-strength (BOLS) correlation to mean-field Hubbard model, i.e., BOLS-HM. Consistency between the BOLS-HM calculation and density functional theory (DFT) calculation on 2D materials verified that (i) bond contractions and potential well depression occur at the edge of graphene, phosphorene, and antimonene nanoribbons; (ii) the physical origin of the band gap opening of graphene, phosphorene, and antimonene nanoribbons lays in the enhancement of edge potentials and hopping integrals due to the shorter and stronger bonds between undercoordinated atoms; (iii) the band gap of 2D material nanoribbons expand as the width decreases due to the increasing under-coordination effects of edges which modulates the conductive behaviors; and (iv) non-bond electrons at the edges and atomic vacancies of 2D material accompanied with the broken bond contribute to the Dirac-Fermi polaron (DFP) with a local magnetic moment.