Abstract
In this work, we present analytical solutions for the wave functions and energy dispersion of zigzag graphene nanoribbons. A nearest neighbor tight-binding model is employed to describe the electronic band structure of graphene nanoribbons. However, an exact analytical solution for the dispersion relation and the wave functions of zigzag nanoribbons cannot be obtained. We propose two approximations of the discrete energies, which are valid for a wide range of nanoribbon indices. Employing these models, selection rules for optical transitions and optical properties of zigzag graphene nanoribbons are studied.
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