A supersymmetric model for graphene

Abreu, Éverton M. C.; Andrade, M. A. De; Assis, Leonardo P. G. De; Helayël-Neto, J. A.; Nogueira, A. L. M. A.; Paschoal, Ricardo C.

doi:10.1007/jhep05(2011)001

Cited by 19 publications

(7 citation statements)

References 50 publications

(102 reference statements)

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“…Due to the observed physical [2], electronic [3] and material science properties [4,5] of graphene, this material has become an extremely promising and an absolutely vital element for basic sciences and modern technology. The interest in graphene is wide, from quantum electrodynamics [4,6], condensed matter [7][8][9] to genomic applications [10,11].…”

Section: Introductionmentioning

confidence: 99%

The ground state of graphene and graphene disordered by vacancies

Kheirabadi¹,

Shafiekhani²

2013

Physica E: Low-dimensional Systems and Nanostructures

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Graphene clusters consisting of 24 to 150 carbon atoms and hydrogen termination at the zigzag boundary edges have been studied, as well as clusters disordered by vacancy(s).Density Function Theory and Gaussian03 software were used to calculate graphene relative stability, desorption energy, band gap, density of states, surface shape, dipole momentum and electrical polarization of all clusters by applying the hybrid exchange-correlation functional Beke-Lee-Yang-Parr. Furthermore, infrared frequencies were calculated for two of them.Different basis sets, 6-31g**, 6-31g* and 6-31g, depending on the sizes of clusters are considered to compromise the effect of this selection on the calculated results. We found that relative stability and the gap decreases according to the size increase of the graphene cluster.Mulliken charge variation increase with the size. For about 500 carbon atoms, a zero HOMO-LUMO gap amount is predicted. Vacancy generally reduces the stability and having vacancy affects the stability differently according to the location of vacancies. Surface geometry of each cluster depends on the number of vacancies and their locations. The energy gap changes as with the location of vacancies in each cluster. The dipole momentum is dependent on the location of vacancies with respect to one another. The carbon-carbon length changes according to each covalence band distance from the boundary and vacancies. Two basis sets, 2 6-31g* and 6-31g**, predict equal amount for energy, gap and surface structure, but charge distribution results are completely different. IntroductionA Graphene sheet is a 2-dimensional honey-comb lattice with carbon atoms occupying the corners of hexagons [1], in which each atom is connected to three other carbon atoms. Due to the observed physical [2], electronic [3] and material science properties [4,5] of graphene, this material has become an extremely promising and an absolutely vital element for basic sciences and modern technology. The interest in graphene is wide, from quantum electrodynamics [4,6], condensed matter [7-9] to genomic applications [10,11]. Several research groups have studied various properties and structures of graphene by different methods, like tight binding [12], semi-empirical [13], molecular dynamics [14-16], Hubbard model [17] and Density Function Theories (DFT) [18, 19]. The use of DFT in the ab initio calculation of molecular properties has increased dramatically. This can be attributed to (i) the development of new and more accurate density functions, (ii) the increasing versatility, efficiency, and availability of DFT codes and most importantly, (iii) the superior ratio of accuracy to efforts exhibited by DFT computations relative to other ab initio methodologies [20]. As a result, DFT has been accepted as one of the most accurate methods of calculation for a wide range of studies about graphene [21-23].It is well understood that the edge effect of finite graphene has a crucial role in its electronic properties [24,25] and DFT method has been used to calculat...

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Section: Introductionmentioning

confidence: 99%

The ground state of graphene and graphene disordered by vacancies

Kheirabadi¹,

Shafiekhani²

2013

Physica E: Low-dimensional Systems and Nanostructures

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“…Therefore, Equation (92) can be reduced to Equation (96), and density of composite can be calculated using rule of mixture as given in Equation (97) [192],…”

Section: Electrical Propertiesmentioning

confidence: 99%

Modeling and Simulation of Graphene Based Polymer Nanocomposites: Advances in the Last Decade

Atif¹,

Inam²

2016

Graphene

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Modeling and simulation allow methodical variation of material properties beyond the capacity of experimental methods. The polymers are one of the most commonly used matrices of choice for composites and have found applications in numerous fields. The stiff and fragile structure of monolithic polymers leads to the innate cracks to cause fracture and therefore the engineering applications of monolithic polymers, requiring robust damage tolerance and high fracture toughness, are not ubiquitous. In addition, when "many-parts" cling together to form polymers, a labyrinth of molecules results, which does not offer to electrons and phonons a smooth and continuous passageway. Therefore, the monolithic polymers are bad conductors of heat and electricity. However, it is well established that when polymers are embedded with suitable entities especially nano-fillers, such as metallic oxides, clays, carbon nanotubes, and other carbonaceous materials, their performance is propitiously improved. Among various additives, graphene has recently been employed as nano-filler to enhance mechanical, thermal, electrical, and functional properties of polymers. In this review, advances in the modeling and simulation of grapheme based polymer nanocomposites will be discussed in terms of graphene structure, topographical features, interfacial interactions, dispersion state, aspect ratio, weight fraction, and trade-off between variables and overall performance.

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“…As we shall explicitly demonstrate, these one dimensional supersymmetries have non-trivial topological charges, a fact probably indicating the existence of a non-linear supersymmetry. The relation of supersymmetry and graphene was also pointed out in [21], but from a completely different point of view. In our study the focus will be on revealing the supersymmetric structures in both gapped and superconducting graphene and relating the corresponding Witten index with the localized modes.…”

Section: Introductionmentioning

confidence: 97%

Extended Supersymmetric Structures in Gapped and Superconducting Graphene

Oikonomou

2015

Int. J. Geom. Methods Mod. Phys.

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In view of the many quantum field theoretical descriptions of graphene in 2 + 1 dimensions, we present another field theoretical feature of graphene, in the presence of defects. Particularly, we shall be interested in gapped graphene in the presence of a domain wall and also for superconducting graphene in the presence of a vortex. As we explicitly demonstrate, the gapped graphene electrons that are localized on the domain wall are associated with four N = 2 one-dimensional supersymmetries, with each pair combining to form an extended N = 4 supersymmetry with non-trivial topological charges. The case of superconducting graphene is more involved, with the electrons localized on the vortex being associated with n one-dimensional supersymmetries, which in turn combine to form an N = 2n extended supersymmetry with non-trivial topological charges. As we shall prove, all supersymmetries are unbroken, a feature closely related to the number of the localized fermions and also to the exact form of the associated operators. In addition, the corresponding Witten index is invariant under compact and odd perturbations.

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A supersymmetric model for graphene

Cited by 19 publications

References 50 publications

The ground state of graphene and graphene disordered by vacancies

The ground state of graphene and graphene disordered by vacancies

Modeling and Simulation of Graphene Based Polymer Nanocomposites: Advances in the Last Decade

Extended Supersymmetric Structures in Gapped and Superconducting Graphene

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