Pdf hydrogen molecule on lithium adsorbed graphene. Using atomic orbitals for periodic dft calculations has many advantages over plane waves like a proper treatment of surfaces, efficient computations of sparse matter, and more direct. Jindal department of physics, panjab university, chandigarh160014, india abinitio calculations have been performed to study the geometry and electronic structure of boron b and nitrogen n doped graphene sheet. In graphene, the density is usually shared equally between a and b. It has been predicted 7 that asymmetry between the onsite energies in the layers leads to a tunable gap between the conduction and valence bands. The tb hamiltonian matrix depends on the value of the nearestneighbor hopping parameter for electrons, which is about 2. Dft energy band structure of abcstacked trilayer graphene in the absence of. Dirac models negativeenergy valenceband states and its conductionband states,4,5 and in a uniform graphene system is readily accounted for by manybody perturbation theory. We have succeeded in opening the band gap, retaining the dirac cones. A comparative study of electronic properties of bulk mos2. We perform an abinitio calculation of the band structure of graphene under uniaxial strain, for deformations up to 10%. The electronic characteristics of graphene disappear completely, as shown in fig. Electronic band structure of armchair and zigzag graphene.
We plot the band structure of pentagraphene which calculated with the generalized gradient approximation functional htch407, about fermi energy. The distinctive bending 9 and binding at hills and valleys have numerous consequences on the properties of graphene and, presumably, of other epitaxial 2d materials, too. I was under the impression that electrons in graphene are described by the dirac equation and not the. Effect of multiple defects and substituted impurities on the. Nov 21, 2015 without dirac cones, graphene loses all its novelty. Graphenebased nanopatch antenna for terahertz radiation. In the metastable geometry, the linear bands of graphene are generally maintained fig. The calculated band structures and density of states showed that both graphite2 h and pure graphene have a zero band gap. Due to only two basis atoms in graphene there is only one pair of. At this moment, the name graphene was not commonly used. Stacked layers of graphene oxide constitute graphite oxide. The electronic band structure of bilayer graphene has been modelled using both density functional theory 1012 and the tight binding model,7,1417. Here, we compare the band gap of pentagraphene with various density functional theory dft methods.
In the band structure of graphene, where exactly the band gap to be. This means that this band is partially filled at the k point, and thus is contributed by both electron. Ajayan 3 1 department of metallurgical engineering, institute of technology, banaras hindu. For instance, the electronic band structure of graphene develops replicas of dirac cones and minibandgaps 11, its. Electronic structure and charge transfer in the tio2 rutile 110. Firstprinciples electronic structure theory, graphene. Dft calculation of band structure of carbon chain pulled. The points \\gamma, k\ and \m\ are used to draw a path in the reciprocal space of graphenes brillouin zone and solver. Abstract the structural and electronic properties of graphene and graphenerelated materials. The electronic band structure of graphene is shown in fig. Transport in graphene nanoribbons quantumatk q2019. Band structure of graphene using tight binding method youtube. Carbon has four valence electrons, of which three are used for the bonds in graphene, graphite, and carbon nanotubes. In interpreting these numbers, one must, however, consider that several publica.
The only relevant kpoints in a 2d hexagonal lattice are g0,0,0, k,0, and. We focus on copper 111 and nickel 111 surfaces adhered to a monolayer of graphene, and. Independent dft estimates 26, 29, 30 indicate that the band gap. Computing the band structure and energy gap of penta. Electronic structures, bonding configurations, and bandgap. Electronic band structure of isolated and bundled carbon.
If you are getting band gap in pristine graphene, you did something wrong. Electronic structure of graphene in kvalley berry phase. Graphene nanoribbons gnrs, also called nanographene ribbons or nanographite ribbons are strips of graphene with width less than 50 nm. Effect of multiple defects and substituted impurities on. Computational modeling of graphene oxide exfoliation and lithium storage characteristics graphene oxide is a two dimensional material obtained by adsorption of oxygen or oxygencontaining groups on graphene.
In interpreting these numbers, one must, however, consider that several publications on graphene appeared before 2006, e. Density functional theory lab handout density function. Tight binding and the nearly free electron approach in this lecture you will learn. In the case of graphene with single vacancy a direct band gap of 1 ev is obtained. Attaching titania clusters of various size to reduced graphene oxide. For the love of physics walter lewin may 16, 2011 duration. The electronic band structure variations of singlewalled carbon nanotubes swcnts using huckletight binding approximation theory are studied. I think there is something wrong here but i do not know how to fix it. Electronic structures, bonding configurations, and band. The calculated band structures and density of states showed that both graphite2. The graphene system with two monovacancies gives rise to an effective indirect band gap pseudo gap of 1 ev. According to the chirality indices, the related expressions for energy dispersion variations of these elements are derived and plotted for zigzag and chiral nanotubes. Band gap engineering by bi intercalation of graphene on ir. We investigate the electronic structure of graphane with hydrogen.
Opening a band gap in silicene and bilayer graphene with an. The tight binding method contd the bands in graphene fbz energy ece 407 spring 2009 farhan rana cornell university graphene and carbon nanotubes. Electronic structure of fewlayer epitaxial graphene on ru. Theoretical studies of graphene and graphenerelated materials involving silicon and carbon by. In this work, we present a systematic numerical analysis of the terahertz radiation scattering on a graphenebased nanopatch antenna. A graphene rectangular patch with length l and width w supported by a dielectric substrate of thickness d is illuminated by a plane wave linearly polarized along the patch length. Dft simulations involve transforming the many body schrodinger equationse to. The associated scattering problem is then solved numerically, and the.
Jul 20, 2010 a linear chain of five atoms of carbon is optimized for the minimum energy to determine the distance between atoms and its band structure is calculated. So opening a gap in graphene, retaining dirac cones has become a challenging task. Band structure of graphene using tight binding method. A dft study gagandeep kaur, shuchi gupta, gaganpreet, and keya dharamvir citation. The only relevant kpoints in a 2d hexagonal lattice are g0,0,0, k,0, and m0,12,0, in units of the reciprocal lattice vectors. Computing the band structure and energy gap of pentagraphene.
The nearestneighbor tightbinding description of graphene was originally developed to study the lowenergy properties of graphite, i. Electronic structure calculation of bulk and monolayer mos 2 has been performed using plane wave pseudopotential method based on density functional theory. All pure dft calculations used the pbe75 exchangecorrelation functional. In this stable geometry, the degeneracy at the dirac point is removed with the energy splitting of 2. Band periodic dft for nanotubes, surfaces, and bulk. Without dirac cones, graphene loses all its novelty. Designing band gap of graphene by b and n dopant atoms. Carbon has four valence electrons, of which three are used for the sp 2 bonds. A linear chain of five atoms of carbon is optimized for the minimum energy to determine the distance between atoms and its band structure is calculated.
Interface structure and mechanics between graphene and metal. Introduction to nanophysics introduction to dft band structure of graphene. Background density functional theory dft is a unique and powerful technique to explore material properties from first principles. The lattice constant of the wellordered hexagonal patches is. Band structure of graphene, massless dirac fermions as low.
Let us start by considering a perfectly at and pure freestanding graphene sheet, with the. A comparative study of electronic properties of bulk mos2 and. Abstract the structural and electronic properties of graphene and. Attaching titania clusters of various size to reduced. Computational modeling of graphene oxide exfoliation and. Graphene is a 2dimensional crystalline allotrope of carbon. Theoretical studies of graphene and graphenerelated. It was realized more than 60 years ago that the electronic band structure of graphene, should it ever be possible to produce it, would be likely to be particularly interesting. Designing band gap of graphene by b and n dopant atoms pooja rani 1and v.
Being a flat monolayer of carbon atoms tightly packed in a twodimensional honeycomb lattice, graphene allows to utilize novel physics in a plethora of potential applications, ranging from ultrahighspeed transistors to. In graphene, carbon atoms are densely packed in a regular hexagonal pattern. There are several quantum effects that alter the propagation of em waves in graphene. Effect of surface doping on the band structure of graphene. For instance, the electronic band structure of graphene develops replicas of. The generalized gradient approximation gga in blyp exchangecorrelation parameterization was used for both final geometry optimization and band structure calculation. Oneshot gw g 0 w 0 correction for precise computations of band structure is applied. The return value of the method is a bands result object. Theoretical studies of graphene and graphenerelated materials involving silicon and carbon by re lwe edwin mapasha supervised by prof nithaya chetty faculty of natural and agricultural sciences submitted in partial ful lment of the requirements for the degree magister scienti.
Figure 3 a shows the band structure, projected density of states pdos, and elf of the asymmetrically deformed graphene systems with l y0. Electronic structures of graphane with vacancies and graphene. Introduction to nanophysics introduction to dft dft provides parameteres for. Depressions by stacking faults in nanorippled graphene on. Jul 26, 20 in particular, dft correctly predicts a zero bandgap closing at the dirac points for pristine graphene 2 and the predicted trends for bandgaps and band structures in graphene based. Graphene synthesis and band gap opening deep jariwala 1, anchal srivastava 2, and pulickel m.
Graphene is a single sheet of carbon atoms arranged in the well known honeycomb structure. Mar 17, 2009 hello all, i have read a few papers lately that have used dft based techniques to investigate metallic adatom adsorption on top of graphene see for instance prb 77, 235430 2008. You should also adjust the symmetry points used for the band structure calculation to avoid the flat segments, which correspond to paths out of the planar graphene brillouin zone. Graphene has recently attracted intense attention of the research community due to its extraordinary mechanical, electronic and optical properties.
A 6x6 graphene supercell with a vacuum space of 11. The magnitude of this gap has been believed to be 1 ev, requiring very low temperatures 0. This exercise is concerned with the bandstructure of the fourth electrons. What is the best way to learn dft density functional theory for beginners. Change of the phase of the wavefunction when the electronic wavefunction is rotated around the dirac point chirality momentum pseudo spin helicity projection of its spin onto the direction of propagation valley pseudospin band index is determined by chirality and valley pseudospin. Band, the accurate periodic density functional theory dft code of the amsterdam modeling suite shares many powerful features with our molecular dft code adf. Band structure of abcstacked graphene trilayers tsapps at nist. The indirect band gap in the bulk mos 2 was found to be 0. Electronic structure from dft calculations phys rev b 77, 035427 2008 phys rev b 82, 245412 2010. Graphene ribbons were introduced as a theoretical model by mitsutaka fujita and coauthors to examine the edge and nanoscale size effect in graphene. The low energy electronic band structure of bilayer graphene.
May 22, 2018 for the love of physics walter lewin may 16, 2011 duration. Dft calculation of band structure of carbon chain pulled from. Then, oneshot gw g 0 w 0 correction for precise computations of band structure is applied. Introduction to the physical properties of graphene. Interface structure and mechanics between graphene and. Here we report on a detailed study of the band structure of. Depressions by stacking faults in nanorippled graphene on metals.
The origin of covalent bonding between two carbon atoms in the fig. Lowenergy physics, diraclike hamiltonian introducing the momentum measured from the k points. Since energy of bands at each k points, we get information about band structure. Bandgap opening by patterning graphene scientific reports. This demonstration shows the electronic structure of both armchair and zigzag graphene nanoribbons obtained by diagonalization of the tightbinding tb hamiltonian matrix in the sampled 1d brillouin zone. Firstprinciples electronic structure theory, graphene calculations zi wang 0463744 verslag van bachelorproject natuur en sterrenkunde, omvang 12 ec, uitgevoerd tussen 01032009 en 09072009. The physical and electronic structure of graphene mono, bi, and trilayers on ru0001 was further investigated theoretically, using density functional theory dft as implemented in vasp. We, through first principles study using density functional theory, have done band gap tuning investigations. An incomplete hexagon with 5 atoms is attached to a linear chain which gives the gap of 1. Electronic structure of graphene and doping effect on sio2. Graphene nanoribbons gnrs, also called nano graphene ribbons or nanographite ribbons are strips of graphene with width less than 50 nm. The principle merit of the dft theory we describe is that it allows this physics to be accounted for in graphene sheets in. Graphene partially substituted with bn patches or strips of different. In particular, dft correctly predicts a zero bandgap closing at the dirac points for pristine graphene 2 and the predicted trends for bandgaps and band structures in graphenebased.
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