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10. Dirac-equation description of the electronic states of graphene with a line defect: Wave-function connection condition

Author

Jiang Li-Wei, Liu Zhe, Zheng Yi-Song, Yu Guodong, and Gao Wen-Zhu

Subjects
Physics, Spinor, Field (physics), Condensed matter physics, Graphene, Condensed Matter Physics, Electronic, Optical and Magnetic Materials, Connection (mathematics), law.invention, symbols.namesake, law, Dirac equation, Line (geometry), symbols, Group velocity, Wave function
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 (1D) electronic state occurs along the line defect. And the electronic group velocity in this quasi-1D electronic state can be readily modulated by applying a strain field around the line defect.

Published
2012

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