Electron transport through honeycomb lattice ribbons with armchair edges

We address electron transport in honeycomb lattice ribbons with armchair edges attached to two semi-infinite one-dimensional metallic electrodes within the tight-binding framework. Here we present numerically the conductance-energy and current-voltage characteristics as functions of the length and width of the ribbons. Our theoretical results predict that for a ribbon with much smaller length and width, so-called a nanoribbon, a gap in the conductance spectrum appears across the energy E=0. While, this gap decreases gradually with the increase of the size of the ribbon, and eventually it almost vanishes. This reveals a transformation from the semiconducting to the conducting material, and it becomes much more clearly visible from our presented current-voltage characteristics.