Eur. Phys. J. B 69, 383-388 (2009)
https://doi.org/10.1140/epjb/e2009-00178-3

Quantum transport in armchair graphene ribbons: analytical tight-binding solutions for propagation through step-like and barrier-like potentials

¹ Space Research Institute of NAS and NSA of Ukraine, 03680 Kyiv, Ukraine
² National Taras Shevchenko University of Kyiv, 03680 Kyiv, Ukraine

Corresponding author: ^a yurkl@ikd.kiev.ua

Received: 28 October 2008
Revised: 5 March 2009
Published online: 21 May 2009

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.