Electronic states of graphene nanoribbons studied with the Dirac equation
Luis Brey,Herbert Fertig +1 more
TLDR
In this paper, the electronic states of narrow graphene ribbons with zigzag and armchair edges were analyzed using the Dirac equation with appropriate boundary conditions, showing that the boundary condition allows a particlelike and a hole-like band with evanescent wave functions confined to the surfaces, which continuously turn into zero energy surface states as the width gets large.Abstract:
We study the electronic states of narrow graphene ribbons (``nanoribbons'') with zigzag and armchair edges. The finite width of these systems breaks the spectrum into an infinite set of bands, which we demonstrate can be quantitatively understood using the Dirac equation with appropriate boundary conditions. For the zigzag nanoribbon we demonstrate that the boundary condition allows a particlelike and a holelike band with evanescent wave functions confined to the surfaces, which continuously turn into the well-known zero energy surface states as the width gets large. For armchair edges, we show that the boundary condition leads to admixing of valley states, and the band structure is metallic when the width of the sample in lattice constant units has the form $3M+1$, with $M$ an integer, and insulating otherwise. A comparison of the wave functions and energies from tight-binding calculations and solutions of the Dirac equations yields quantitative agreement for all but the narrowest ribbons.read more
Citations
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Substrate-induced bandgap opening in epitaxial graphene
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References
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Experimental observation of the quantum Hall effect and Berry's phase in graphene
TL;DR: In this paper, an experimental investigation of magneto-transport in a high-mobility single layer of Graphene is presented, where an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene is observed.
Journal Article
Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
TL;DR: An experimental investigation of magneto-transport in a high-mobility single layer of graphene observes an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene.
Book
Physical properties of carbon nanotubes
TL;DR: In this paper, an introductory textbook for graduate students and researchers from various fields of science who wish to learn about carbon nanotubes is presented, focusing on the basic principles behind the physical properties and giving the background necessary to understand the recent developments.