Low-energy electron transmission in a partially unzipped zigzag nanotube

Based on the nearest-neighbor tight-binding approximation, we present exact analytical expressions for electron transmission in nanotube/ribbon junctions, generated by incomplete unzipping of zigzag nanotubes. By assuming one-dimer-line difference in the widths of the leads, it is demonstrated that such a contact exhibits zero backscattering of low-energy electrons entering from the graphene side of the junction. We also show that a zigzag nanotube section sandwiched between two armchair graphene ribbons is completely transparent for incident low-energy electrons. Possible application of the results to nanosensor engineering is also included.