Energy levels of triangular and hexagonal graphene quantum dots: A comparative study between the tight-binding and Dirac equation approach
- 7 December 2011
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 84 (24), 245403
- https://doi.org/10.1103/physrevb.84.245403
Abstract
The Dirac equation is solved for triangular and hexagonal graphene quantum dots for different boundary conditions in the presence of a perpendicular magnetic field. We analyze the influence of the dot size and its geometry on their energy spectrum. A comparison between the results obtained for graphene dots with zigzag and armchair edges, as well as for infinite-mass boundary condition, is presented and our results show that the type of graphene dot edge and the choice of the appropriate boundary conditions have a very important influence on the energy spectrum. The single-particle energy levels are calculated as a function of an external perpendicular magnetic field that lifts degeneracies. Comparing the energy spectra obtained from the tight-binding approximation to those obtained from the continuum Dirac equation approach, we verify that the behavior of the energies as a function of the dot size or the applied magnetic field are qualitatively similar, but in some cases quantitative differences can exist.Keywords
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