Spectrum of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi></mml:math>electrons in graphene as an alternant macromolecule and its specific features in quantum conductance

Onipko, Alexander

doi:10.1103/physrevb.78.245412

Cited by 54 publications

(89 citation statements)

References 65 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, it is worth noting that the electronic states of armchair nanotubes with finite length N and its circumstance L y a T can be analytically obtained if we assume that L y has a finite value. The case of the open boundary condition in the longitudinal direction was recently studied using the monomer Green's function approach [100,101].…”

Section: Discussionmentioning

confidence: 99%

Electronic states of graphene nanoribbons and analytical solutions

Wakabayashi

Sasaki

Nakanishi

et al. 2010

Science and Technology of Advanced Materials

403

429

View full text Add to dashboard Cite

Graphene is a one-atom-thick layer of graphite, where low-energy electronic states are described by the massless Dirac fermion. The orientation of the graphene edge determines the energy spectrum of π-electrons. For example, zigzag edges possess localized edge states with energies close to the Fermi level. In this review, we investigate nanoscale effects on the physical properties of graphene nanoribbons and clarify the role of edge boundaries. We also provide analytical solutions for electronic dispersion and the corresponding wavefunction in graphene nanoribbons with their detailed derivation using wave mechanics based on the tight-binding model. The energy band structures of armchair nanoribbons can be obtained by making the transverse wavenumber discrete, in accordance with the edge boundary condition, as in the case of carbon nanotubes. However, zigzag nanoribbons are not analogous to carbon nanotubes, because in zigzag nanoribbons the transverse wavenumber depends not only on the ribbon width but also on the longitudinal wavenumber. The quantization rule of electronic conductance as well as the magnetic instability of edge states due to the electron-electron interaction are briefly discussed.

show abstract

Section: Discussionmentioning

confidence: 99%

Electronic states of graphene nanoribbons and analytical solutions

Wakabayashi

Sasaki

Nakanishi

et al. 2010

Science and Technology of Advanced Materials

403

429

View full text Add to dashboard Cite

show abstract

“…Figure 3 . This is because in these positions the wave function of armchair ribbons vanishes or is very small 40,41 (Sec. III B), and therefore the defect is not "felt" by the incoming states.…”

Section: A Effect Of a Single Defectmentioning

confidence: 99%

“…The symmetrical aGNR has states localized on the atoms with indices ρ and λ with the energies E = ±1. 40 Thus the expression for the retarded Green's function in symmetrical aGNR is…”

Section: B Analytical Expressions For Transmission Of Electrons In Mmentioning

confidence: 99%

Effect of zigzag and armchair edges on the electronic transport in single-layer and bilayer graphene nanoribbons with defects

2013

View full text Add to dashboard Cite

We study electronic transport in monolayer and bilayer graphene with single and many short-range defects focusing on the role of edge termination (zigzag versus armchair). Within the tight-binding approximation, we derive analytical expressions for the transmission amplitude in monolayer graphene nanoribbons with a single short-range defect. The analytical calculations are complemented by exact numerical transport calculations for monolayer and bilayer graphene nanoribbons with a single and many short-range defects and edge disorder. We find that for the case of the zigzag edge termination, both monolayer and bilayer nanoribbons in a single-and few-mode regime remain practically insensitive to defects situated close to the edges. In contrast, the transmission of both armchair monolayer and bilayer nanoribbons is strongly affected by even a small edge defect concentration. This behavior is related to the effective boundary condition at the edges, which, respectively, does not and does couple valleys for zigzag and armchair nanoribbons. In the many-mode regime and for sufficiently high defect concentration, the difference of the transmission between armchair and zigzag nanoribbons diminishes. We also study resonant features (Fano resonances) in monolayer and bilayer nanoribbons in a single-mode regime with a short-range defect. We discuss in detail how an interplay between the defect's position at different sublattices in the ribbons, the defect's distance to the edge, and the structure of the extended states in ribbons with different edge termination influence the width and the energy of Fano resonances.

show abstract

“…Going back to the original wave vectors k x and k y , the band structure of bilayer graphene tubes and ribbons when V = 0 as in Ref. 24 can be summarized by the equation…”

Section: Band Structure Near the Fermi Energymentioning

confidence: 99%

“…Analytic calculations for the electronic structure of GNRs have been reported in Refs. [21][22][23][24][25]. The electronic structure of bilayer graphene was addressed in Refs.…”

Section: Introductionmentioning

confidence: 99%

Spectrum ofπelectrons in bilayer graphene nanoribbons and nanotubes: An analytical approach

2011

View full text Add to dashboard Cite

We present an analytical description of π electrons of a finite-size bilayer graphene within a framework of the tight-binding model. The bilayered structures considered here are characterized by a rectangular geometry and have a finite size in one or both directions with armchair-and zigzag-shaped edges. We provide an exact analytical description of the spectrum of π electrons in the zigzag and armchair bilayer graphene nanoribbons and nanotubes. We analyze the dispersion relations, the density of states, and the conductance quantization.

show abstract

Spectrum ofπelectrons in graphene as an alternant macromolecule and its specific features in quantum conductance

Cited by 54 publications

References 65 publications

Electronic states of graphene nanoribbons and analytical solutions

Electronic states of graphene nanoribbons and analytical solutions

Effect of zigzag and armchair edges on the electronic transport in single-layer and bilayer graphene nanoribbons with defects

Spectrum ofπelectrons in bilayer graphene nanoribbons and nanotubes: An analytical approach

Contact Info

Product

Resources

About