Abstract
This work reviews the current progress of tight-binding methods and the recent edge-modified mean-field Hubbard model. Undercoordinated atoms and nonbonding electrons exist widely in nanomaterials and in network-structural materials with their impact under-estimated. A quantum theory was proposed to calculate the under-coordinated effects on the electronic structure of materials by incorporating bond order-length-strength (BOLS) correlation theory 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) nonbond 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.
Highlights
Once the size of nanomaterials decreases, the ratio of under-coordinated atoms located at surface, edges, and defects increase compared to the total atomic number
bond order-length-strength (BOLS)-Hubbard Model in 2D Materials constant, and the extensibility of a solid can change with the solid size [14,15,16]
Under the light shed by BOLS theory, we will explore the mysteries brought by broken bond and non-bond of nanomaterial
Summary
Once the size of nanomaterials decreases, the ratio of under-coordinated atoms located at surface, edges, and defects increase compared to the total atomic number. CN Imperfection Induced Quantum Trapping According to the BOLS correlation theory, CN imperfection at edges of low-dimensional nanostructures or at surface skin of 0-D nanoparticles causes the remaining bonds of the under-coordinated atoms to contract spontaneously with an association of bond strength gain, which in turn causes potential well depression with a consequence of localized densification of charge, energy, and mass. In the present BOLS-HM, we took the following relations of effective coordination number (z), bond length (d), single bond energy (E), potential (V), and Hamiltonian integrals α an βijvv′ into consideration, the modification of under-coordinated site i to the bulk B can be expressed as, Cz (zi ). The following relations of effective coordination number (z), bond coefficient (Cz), single bond energy (E), potential (V), and hopping integral were be taken into consideration in the present BOLS-HM.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
