Abstract
Based on the nearest-neighbor tight-binding approximation, we present exact analytical expressions for transmission coefficients through piecewise constant step-like and barrier-like electrostatic potentials. In the case of single mode propagation through semiconducting ribbon families our analytical solutions predict a new kind of resonances. Its features substantially change the behavior of the transmission coefficients in the range of moderate potentials, which become family-dependent. For semimetal ribbons our approach predicts no unit propagation. The non-zero backscattering is derived to be proportional as the square of the potential amplitude applied.
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Klymenko, Y., Shevtsov, O. Quantum transport in armchair graphene ribbons: analytical tight-binding solutions for propagation through step-like and barrier-like potentials. Eur. Phys. J. B 69, 383–388 (2009). https://doi.org/10.1140/epjb/e2009-00178-3
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DOI: https://doi.org/10.1140/epjb/e2009-00178-3