Hybridization bond states and band structure of graphene: a simple approach

Abstract

This article reviews the basic theoretical aspects of graphene in order to contribute to making teaching easier and more understandable for those who still cannot understand it in an abstract way. This work presents the basic aspects of sp2 hybridization concepts from a quantum approach, which consists in obtaining the states for the sigma bonds from the orientation of the carbon atoms close to another carbon atom that is our reference point in the crystal lattice. Furthermore, we calculate the band structure of graphene by using the Tight-Binding Model, which can give us a good approximation to the energy levels as a function of the wave vector. This is for students interested in the topics of the solid-state and is approached in a simple and understandable way step by step to nally obtain the structure of bands of the primitive cell of one monolayer of graphene. Additionally, we calculate the High Symmetry points of the rst Brillouin zone and the analysis around the K points to obtain the well-known Dirac cones. The intention of this work is to show that this topic can be less abstract than it seems.

Ferromagnetic Elements in Two‐Dimensional Materials: 2D Magnets and Beyond

“…[204][205][206] It is well known that magnetic moments have their origin in the presence of unpaired d and f electrons, while graphene, similar to every carbon system with sp, sp 2 , and sp 3 hybridization, lacks unpaired electrons. [207][208][209] Therefore, due to the lack of unpaired electrons, graphene is known as a pure diamagnet. [210,211] Nevertheless, there is a need for the induction of ferromagnetism to become applicable in the domain of spintronics.…”

Towards graphene-based asymmetric diodes: a density functional tight-binding study

“…where f is the Fermi energy and T L /T R is the electron temperature of the le/right electrode, where the L and R electrodes are the source and drain, respectively. T s (E) is the transmission coefficient for spin component s. Finally, the chemical potentials of the right/le electrode and V bias can be dened by eqn ( 4)- (7),…”

“…The C–C bonds in graphene have an intermediate length between C–C sp 3 and C–C sp 2 bonds. 7 Graphene is a perfect two-dimensional crystal with conductivity mediated by electrons with zero effective mass. These features make graphene a promising material for a new generation of solid-state electronics, 8 especially for applications in radio frequency electronics, 9 optoelectronics, 10 and sensor systems.…”

Low-temperature green synthesis of few-layered graphene sheets from pomegranate peels for supercapacitor applications

“…Graphene is a two-dimensional planar structure of s hybridized carbon atoms 1 arranged in a honeycomb crystal lattice 2 with an inter-layer spacing of 3.35 Å. Graphite crystals, nanotubes, and fullerenes can be formed from graphene by stacking layers, rolling in a specific direction, or wrapping them into a ball 3 . Graphene is a unique nanomaterial with zero band gap 4 and the only carbon allotrope where carbon atoms are tightly bonded to their neighbors by a unique electronic cloud deviating slightly from quantum mechanical principles 5 .…”

“…Graphene is a unique nanomaterial with zero band gap 4 and the only carbon allotrope where carbon atoms are tightly bonded to their neighbors by a unique electronic cloud deviating slightly from quantum mechanical principles 5 . These electrons move freely between the 2pz orbitals 1 , explaining why graphene exhibits unparalleled electrical conductivity 5 .…”