Dynamical gap generation in graphene nanoribbons: An effective relativistic field theoretical model

Abstract. We present a unified description of the excitonic properties of four monolayer transition-metal dichalcogenides (TMDC's) using an equation of motion method for deriving the Bethe-Salpeter equation in momentum space. Our method is able to cope with both continuous and tight-binding Hamiltonians, and is less computational demanding than the traditional first-principles approach. We show that the role of the exchange energy is essential to obtain a good description of the binding energy of the excitons. The exchange energy at the Γ−point is also essential to obtain the correct position of the C-exciton peak. Using our model we obtain a good agreement between the Rydberg series measured for WS 2 . We discuss how the absorption and the Rydberg series depend on the doping. Choosing r 0 and the doping we obtain a good qualitative agreement between the experimental absorption and our calculations for MoS 2 and WS 2 . We also derive a semi-analytical version of Ellitot's formula for TMDC's.arXiv:1704.00975v1 [cond-mat.mes-hall]

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“…For graphene this procedure is used to study the possibility of dynamical generation of a gap in the spectrum [30,31].…”

Section: Calculation Of the Exchange Energymentioning

confidence: 99%

Excitonic effects in the optical properties of 2D materials:an equation of motion approach

et al. 2017

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“…10,11 Numerous theoretical [12][13][14][15][16][17][18][19][20][21] as well as experimental [22][23][24][25][26][27] studies have shown that this band gap depends on the GNR type, i.e., on its width as well as on the shape of its edges, e.g., zigzag or armchair, much like in carbon nanotubes. While the inverse power law for the width dependence of the band gap is found to be universal in nanoribbons of several tens of nanometers width, 22 the influence of the GNR's chiral vector becomes more and more important as the ribbons become as narrow a) Electronic mail: bronner@uni-heidelberg.de as a few carbon atoms.…”

Section: Introductionmentioning

confidence: 99%

Electronic structure changes during the surface-assisted formation of a graphene nanoribbon

Bronner

Utecht

Haase

et al. 2014

The Journal of Chemical Physics

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High conductivity and a tunability of the band gap make quasi-one-dimensional graphene nanoribbons (GNRs) highly interesting materials for the use in field effect transistors. Especially bottom-up fabricated GNRs possess well-defined edges which is important for the electronic structure and accordingly the band gap. In this study we investigate the formation of a sub-nanometer wide armchair GNR generated on a Au(111) surface. The on-surface synthesis is thermally activated and involves an intermediate non-aromatic polymer in which the molecular precursor forms polyanthrylene chains. Employing angle-resolved two-photon photoemission in combination with density functional theory calculations we find that the polymer exhibits two dispersing states which we attribute to the valence and the conduction band, respectively. While the band gap of the non-aromatic polymer obtained in this way is relatively large, namely 5.25 ± 0.06 eV, the gap of the corresponding aromatic GNR is strongly reduced which we attribute to the different degree of electron delocalization in the two systems.

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“…This model is well suited to describe various disorder phenomena such as topological defects, doping defects or distortions of the lattice honeycomb. Within this framework, carbon nanotubes and graphene have been studied and their quantum properties have been reproduced 42,43 . In the present study, inspired by the work of [39][40][41] , we explore how charge confinement and Klein tunneling can be induced by certain types of defects, and examine how defects -modeled as 1D potential barriers -can be mapped into fermionic operators.…”

Section: Introductionmentioning

confidence: 99%

Charge confinement and Klein tunneling from doping graphene

Popovici¹,

Oliveira²,

Paula³

et al. 2012

Phys. Rev. B

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In the present work, we investigate how structural defects in graphene can change its transport properties. In particular, we show that breaking of the sublattice symmetry in a graphene monolayer overcomes the Klein effect, leading to confined states of massless Dirac fermions. Experimentally, this corresponds to chemical bonding of foreign atoms to carbon atoms, which attach themselves to preferential positions on one of the two sublattices. In addition, we consider the scattering off a tensor barrier, which describes the rotation of the honeycomb cells of a given region around an axis perpendicular to the graphene layer. We demonstrate that in this case the intervalley mixing between the Dirac points emerges, and that Klein tunneling occurs.

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Dynamical gap generation in graphene nanoribbons: An effective relativistic field theoretical model

Cited by 16 publications

References 28 publications

Excitonic effects in the optical properties of 2D materials:an equation of motion approach

Excitonic effects in the optical properties of 2D materials:an equation of motion approach

Electronic structure changes during the surface-assisted formation of a graphene nanoribbon

Charge confinement and Klein tunneling from doping graphene

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