Hall conductance in graphene with point defects

Date
2013
Authors
İslamoǧlu, S.
Oktel, M. Ö.
Gülseren, O.
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Source Title
Journal of Physics Condensed Matter
Print ISSN
0953-8984
Electronic ISSN
1361-648X
Publisher
Volume
25
Issue
5
Pages
1 - 10
Language
English
Type
Article
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Abstract

We investigate the Hall conductance of graphene with point defects within the Kubo formalism, which allows us to calculate the Hall conductance without constraining the Fermi energy to lie in a gap. For pure graphene, which we model using a tight-binding Hamiltonian, we recover both the usual and the anomalous integer quantum Hall effects depending on the proximity to the Dirac points. We investigate the effect of point defects on Hall conduction by considering a dilute but regular array of point defects incorporated into the graphene lattice. We extend our calculations to include next nearest neighbor hopping, which breaks the bipartite symmetry of the lattice. We find that impurity atoms which are weakly coupled to the rest of the lattice result in gradual disappearance of the high conductance value plateaus. For such impurities, especially for vacancies which are decoupled from the lattice, strong modification of the Hall conductance occurs near the E = 0 eV line, as impurity states are highly localized. In contrast, if the impurities are strongly coupled, they create additional Hall conductance plateaus at the extremum values of the spectrum, signifying separate impurity bands. Hall conductance values within the original spectrum are not strongly modified.

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Keywords
Conductance values, Dirac point, Graphene lattices, Hall conductance, Impurity atoms, Impurity bands, Impurity state, Nearest neighbor hopping, Regular array, Tight-binding Hamiltonians, Impurities, Point defects, Quantum Hall effect, Graphene
Citation
Published Version (Please cite this version)