We report a first-principles study on electronic structures of the deformed armchair graphene nanoribbons (AGNRs). The variation of the energy gap of AGNRs as a function of uniaxial strain displays a zigzag pattern, which indicates that the energy gaps of AGNRs can be effectively tuned. The spatial distributions of two occupied and two empty subbands close to the Fermi level are swapped under different strains. The tunable width of energy gaps becomes narrower as increasing the width of AGNRs. Our simulations with tight binding approximation, including the nearest neighbor hopping integrals between $pi$- orbitals of carbon atoms, reproduce these results by first-principles calculations. One simple empirical formula is obtained to describe the scaling behavior of the maximal value of energy gap as a function of the width of AGNRs.
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