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Electronic state of zigzag graphene nanoribbons

Deng Wei-Yin Zhu Rui Deng Wen-Ji

Electronic state of zigzag graphene nanoribbons

Deng Wei-Yin, Zhu Rui, Deng Wen-Ji
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Publishing process
  • Received Date:  16 October 2012
  • Accepted Date:  17 November 2012
  • Published Online:  05 March 2013

Electronic state of zigzag graphene nanoribbons

  • 1. Department of Physics, South China University of Technology, Guangzhou 510641, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11004063), and the Fundamental Research Funds for the Central Universities, China (Grant No. 2012ZZ0076).

Abstract: Based on the tight-binding model, the electronic state and band of zigzag graphene nanoribbons are given analytically by a new method. The results show that there are only two kinds electronic states, i.e., the standing wave state and edge state. For the standing wave state, the wave function is sine function and the vector is real; for the edge state, the wave function is hyperbolic sine function and the vector is complex, whose real part is 0 or π/2. The energy band is composed of the energy of standing wave state and the energy of edge state. The accurate ranges of infinite direction wave vector and energy of the edge state are deduced. Then we discuss the transition point between the edge state and the standing wave state and find that the two kinds of electronic states tend to the linear relationship regarding the site of carbon lattice in different ways at the phase transition point. When the width of two restricted boundary goes to infinity, the result of the limited graphene tends to the infinite case.

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