Electronic states of graphene grain boundaries

Mesaroš, Andrej; Papanikolaou, Stefanos; Flipse, Cfj Kees; Sadri, Darius; Zaanen, Jan

doi:10.1103/physrevb.82.205119

Cited by 77 publications

(73 citation statements)

References 43 publications

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“…We comment here that simpler topological defects (e.g., a single 56 pentagon, heptagon, or pentagonheptagon pair embedded in the honeycomb lattice) are often described 57,58 (at zero magnetic field) in the continuum DW approach via a gauge field (an additional vector potential) resembling the one generated by an AharonovBohm magnetic-flux solenoid. The generalization of this gauge-field modification of the DW equation to multiple topological defects may provide a better overall agreement with the TB results.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…However, concerning the unique features found via TB calculations, only the feature of the Halperin-type edge states with an enhanced density spectrum (D2 region) maintains also in the continuum spectra; the rest of the special reczag features [see (III), (IV), and (VI) above] are missing in the continuum-DW spectrum. Due to this major discrepancy between the TB and continuum descriptions, we are led to conclude that the linearized DW equation fails to capture essential nonlinear physics (i.e., a nonlinear dispersion of energy versus momentum 54 coexisting with the Dirac cone), resulting from the introduction of a nontrivial (multiple) topological defect [55][56][57][58][59] (e.g., reconstructed reczag edge) in the honeycomb graphene lattice.…”

Section: Main Findingsmentioning

confidence: 99%

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Graphene flakes with defective edge terminations: Universal and topological aspects, and one-dimensional quantum behavior

2012

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Systematic tight-binding investigations of the electronic spectra (as a function of the magnetic field) are presented for trigonal graphene nanoflakes with reconstructed zigzag edges, where a succession of pentagons and heptagons, that is 5-7 defects, replaces the hexagons at the zigzag edge. For nanoflakes with such reczag defective edges, emphasis is placed on topological aspects and connections underlying the patterns dominating these spectra. The electronic spectra of trigonal graphene nanoflakes with reczag edge terminations exhibit certain unique features, in addition to those that are well known to appear for graphene dots with zigzag edge termination. These unique features include breaking of the particle-hole symmetry, and they are associated with nonlinear dispersion of the energy as a function of momentum, which may be interpreted as nonrelativistic behavior. The general topological features shared with the zigzag flakes include the appearance of energy gaps at zero and low magnetic fields due to finite size, the formation of relativistic Landau levels at high magnetic fields, and the presence between the Landau levels of edge states (the socalled Halperin states) associated with the integer quantum Hall effect. Topological regimes, unique to the reczag nanoflakes, appear within a stripe of negative energies ε b < ε < 0, and along a separate feature forming a constant-energy line outside this stripe. The ε b lower bound specifying the energy stripe is independent of size.Prominent among the patterns within the ε b < ε < 0 energy stripe is the formation of threemember braid bands, similar to those present in the spectra of narrow graphene nanorings; they are associated with Aharonov-Bohm-type oscillations, i.e., the reczag edges along the three sides of the triangle behave like a nanoring (with the corners acting as scatterers) enclosing the magnetic flux through the entire area of the graphene flake. Another prominent feature within the ε b < ε < 0 energy stripe is a subregion of Halperin-type edge states of enhanced density immediately below the zero-Landau level. Furthermore, there are features resulting from localization of the Dirac quasiparticles at the corners of the polygonal flake.A main finding concerns the limited applicability of the continuous Dirac-Weyl equation, since the latter does not reproduce the special reczag features. Due to this discrepancy between the tightbinding and continuum descriptions, one is led to the conclusion that the linearized Dirac-Weyl equation fails to capture essential nonlinear physics resulting from the introduction of a multiple topological defect in the honeycomb graphene lattice.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: Main Findingsmentioning

confidence: 99%

Graphene flakes with defective edge terminations: Universal and topological aspects, and one-dimensional quantum behavior

2012

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“…This method is now capable of producing single graphene grains reaching the centimeter scale [13][14][15] , but faster CVD growth yields much smaller grains, resulting in a material that is polycrystalline 15 . In polycrystalline graphene, the grain boundaries (GBs) between misoriented grains consist of a series of non-hexagonal rings [16][17][18] that can impede charge transport through the material [19][20][21] . In addition, GBs tend to be more chemically reactive than pristine graphene, which can also strongly impact charge transport, making this material interesting for gas sensing applications 22,23 .…”

Section: Since Its Experimental Isolation In 2004mentioning

confidence: 99%

Grain boundary-induced variability of charge transport in hydrogenated polycrystalline graphene

Vargas¹,

Falkenberg²,

Soriano³

et al. 2017

2D Mater.

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Chemical functionalization has proven to be a promising means of tailoring the unique properties of graphene. For example, hydrogenation can yield a variety of interesting effects, including a metal-insulator transition or the formation of localized magnetic moments. Meanwhile, graphene grown by chemical vapor deposition is the most suitable for large-scale production, but the resulting material tends to be polycrystalline. Up to now there has been relatively little focus on how chemical functionalization, and hydrogenation in particular, impacts the properties of polycrystalline graphene. In this work, we use numerical simulations to study the electrical properties of hydrogenated polycrystalline graphene. We find a strong correlation between the spatial distribution of the hydrogen adsorbates and the charge transport properties. When the hydrogen is confined to the grain boundaries there is little impact on charge transport, while a uniform distribution of hydrogen yields a significant degradation of the electronic mobility. This difference is related to the resonant impurity states induced by the hydrogen adsorbates; these states can form when the hydrogen is in the pristine graphene grains, but not when the hydrogen is within the grain boundary. These results suggest that one can tune the electrical transport of polycrystalline graphene through selective hydrogen functionalization, and they also have important implications for hydrogeninduced magnetization and spin lifetime of this material.

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“…The development of practical methods for the synthesis of large area single-and few-layer graphenes [1][2][3][4] is focusing attention on the influence of grain boundaries on their electronic behavior [3][4][5][6][7] . These extended defects have been studied theoretically to understand their reconstruction of the low energy Dirac spectra and their signatures in transport [7][8][9][10][11][12][13][14] . In this Rapid Communication we consider the family of "zero angle" grain boundaries (ZGB's) and study their electronic properties using a new quantum geometric formulation.…”

mentioning

confidence: 99%

“…Our preliminary work indicates that this distinction is important and can determine the topological character of the boundary 20 . It will also be useful to augment this topological analysis to address the consequences of local symmetry breaking perturbations (presumed to be weak) that inevitably occur in atomistic models that suggest structure-specific spectral reconstruction near the neutrality point [7][8][9][10][11][12][13][14] . Finally the presence of flat or weakly dispersing bands near charge neutrality invites an investigation of its interaction-induced instabilities.…”

mentioning

confidence: 99%

Zero modes on zero-angle grain boundaries in graphene

Phillips

Mele

2015

Phys. Rev. B

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Electronic states confined to zero angle grain boundaries in single layer graphene are analyzed using topological band theoretic arguments. We identify a hidden chiral symmetry which supports symmetry protected zero modes in projected bulk gaps. These branches occupy a finite fraction of the interface-projected Brillouin zone and terminate at bulk gap closures, manifesting topological transitions in the occupied manifolds of the bulk systems that are joined at an interface. These features are studied by numerical calculations on a tight binding lattice and by analysis of the geometric phases of the bulk ground states..

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Electronic states of graphene grain boundaries

Cited by 77 publications

References 43 publications

Graphene flakes with defective edge terminations: Universal and topological aspects, and one-dimensional quantum behavior

Graphene flakes with defective edge terminations: Universal and topological aspects, and one-dimensional quantum behavior

Grain boundary-induced variability of charge transport in hydrogenated polycrystalline graphene

Zero modes on zero-angle grain boundaries in graphene

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