Quantum transport in honeycomb lattice ribbons with armchair and zigzag   edges coupled to semi-infinite linear chain leads
  We study quantum transport in honeycomb lattice ribbons with either armchair or zigzag edges. The ribbons are coupled to semi-infinite linear chains serving as the input and output leads and we use a tight-binding Hamiltonian with nearest-neighbor hops. For narrow ribbons we find transmission gaps for both types of edges. The center of the gap is at the middle of the band in ribbons with armchair edges. This symmetry is due to a property satisfied by the matrices in the resulting linear problem. In ribbons with zigzag edges the gap center is displaced to the right of the middle of the band. We also find transmission oscillations and resonances within the transmitting region of the band for both types of edges. Extending the length of a ribbon does not affect the width of the transmission gap, as long as the ribbon's length is longer than a critical value when the gap can form. Increasing the width of the ribbon, however, changes the width of the gap. In armchair edges the gap is not well-defined because of the appearance of transmission resonances while in zigzag edges the gap width systematically shrinks as the width of the ribbon is increased. We also find only evanescent waves within the gap and both evanescent and propagating waves in the transmitting regions. 
Eduardo Cuansing and Jian-Sheng Wang