On electronic conductance of partially unzipped armchair nanotubes: further analysis

Abstract

An investigation of the electronic conductance, based on the nearest-neighbor tight-binding approximation for non-interacting π-electrons, is presented for a junction generated by partial unzipping along the zigzag direction of armchair nanotube. An exact solution of the transmission problem has been found through the scalar discrete Wiener–Hopf method, by exploiting a symmetry of the structure for the reduction of 2 × 2 matrix kernel. The electronic probability distribution, far away from the junction on either side of it, is obtained in closed form via mode-matching. As the main result of the paper, an analytical expression for the reflection and transmission coefficients, as well as the scattering matrix, previously obtained via computational methods in earlier studies, is provided using the Chebyshev polynomials. It is found that the highly simplified nearest neighbor tight binding model of the ribbon/tube junction does not allow a mixing of the parity based on even and odd modes. The paper includes several graphical illustrations and analytical derivations.