Title
Geometry and edge effects on the energy levels of graphene quantum rings : a comparison between tight-binding and simplified Dirac models Geometry and edge effects on the energy levels of graphene quantum rings : a comparison between tight-binding and simplified Dirac models
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
Lancaster, Pa ,
Subject
Physics
Source (journal)
Physical review : B : condensed matter and materials physics. - Lancaster, Pa, 1998 - 2015
Volume/pages
89(2014) :7 , p. 1-12
ISSN
1098-0121
1550-235X
1098-0121
Article Reference
075418
Carrier
E-only publicatie
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
We present a systematic study of the energy spectra of graphene quantum rings having different geometries and edge types in the presence of a perpendicular magnetic field. Results are obtained within the tight-binding (TB) and Dirac models and we discuss which features of the former can be recovered by using the approximations imposed by the latter. Energy levels of graphene quantum rings obtained by diagonalizing the TB Hamiltonian are demonstrated to be strongly dependent on the rings geometry and the microscopical structure of the edges. This makes it difficult to recover those spectra by the existing theories that are based on the continuum (Dirac) model. Nevertheless, our results show that both approaches (i.e., TB and Dirac model) may provide similar results, but only for very specific combinations of ring geometry and edge types. The results obtained by a simplified model describing an infinitely thin circular Dirac ring show good agreement with those obtained for hexagonal and rhombus armchair graphene rings within the TB model. Moreover, we show that the energy levels of a circular quantum ring with an infinite mass boundary condition obtained within the Dirac model agree with those for a ring defined by a ring-shaped staggered potential obtained within the TB model.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/920025/7203.pdf
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