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Dirac-equation description of the electronic states of graphene with a line defect: Wave-function connection condition.
- Source :
-
Physical Review B: Condensed Matter & Materials Physics . Oct2012, Vol. 86 Issue 16, p1-8. 8p. - Publication Year :
- 2012
-
Abstract
- The presence of an extended line defect in graphene brings about some interesting electronic properties to such a truly two-dimensional (2D) carbon material, such as the energy-band engineering and valley filtering. By establishing an appropriate connection condition for the spinor wave function across the line defect, we find that the massless Dirac equation is still a valid theoretical model to describe low-energy electronic properties of the line defect embedded graphene structure. To check the validity of the wave-function connection condition, we take two kinds of line defect embedded graphene structures as examples to study the low-energy electronic states by solving the Dirac equation. First, for a line defect embedded zigzag-edged graphene nanoribbon, we obtain analytical results about the subband dispersion and eigenwave function, which coincide well with the numerical results from the tight-binding approach. Then, for a 2D graphene embedded with an extended line defect, we get an exact expression about the valley polarized electronic transmission probability, which demonstrates the simple result estimated previously in the zero-energy limit. More interestingly, our analytical result indicates that in such a 2D graphene structure a quasi-one-dimensional (ID) electronic state occurs along the line defect. And the electronic group velocity in this quasi-ID electronic state can be readily modulated by applying a strain field around the line defect. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10980121
- Volume :
- 86
- Issue :
- 16
- Database :
- Academic Search Index
- Journal :
- Physical Review B: Condensed Matter & Materials Physics
- Publication Type :
- Academic Journal
- Accession number :
- 83990869
- Full Text :
- https://doi.org/10.1103/PhysRevB.86.165433