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Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities

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Hall conductance in graphene with point defects.

S İslamoğlu¹, M Ö Oktel, O Gülseren

¹Department of Physics, Bilkent University, 06800 Ankara, Turkey. selcen@fen.bilkent.edu.tr

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|January 10, 2013

Summary

Point defects in graphene significantly alter Hall conductance. Weakly coupled impurities cause plateau disappearance, while strongly coupled impurities create new plateaus, impacting quantum Hall effects.

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Area of Science:

Condensed Matter Physics
Materials Science
Quantum Mechanics

Background:

Graphene exhibits quantum Hall effects, sensitive to lattice structure and defects.
The Kubo formalism enables Hall conductance calculations without Fermi energy gap constraints.

Purpose of the Study:

Investigate Hall conductance in graphene with point defects.
Analyze the impact of impurity coupling and lattice symmetry on quantum Hall phenomena.

Main Methods:

Utilized the Kubo formalism for Hall conductance calculations.
Modeled graphene with a tight-binding Hamiltonian, including next-nearest neighbor hopping.
Considered dilute, regular arrays of point defects.

Main Results:

Pure graphene shows usual and anomalous integer quantum Hall effects near Dirac points.
Weakly coupled impurities, especially vacancies, drastically modify Hall conductance near E=0 eV due to localized impurity states.
Strongly coupled impurities form impurity bands, creating new Hall conductance plateaus at spectral extrema without significantly altering original spectrum values.

Conclusions:

Point defect characteristics (coupling strength, localization) critically determine Hall conductance behavior in graphene.
Graphene's quantum Hall effects are robust but can be tuned by controlled introduction of specific types of point defects.