Eigenstates and transmission coefficients of finite-sized carbon nanotubes

Abstract

The tight-binding eigenstates of isolated finite-sized zigzag and armchair nanotubes are obtained analytically using the transfer matrix method. Edge states are encountered for zigzag tubes but not for armchair tubes. Inclusion of curvature leads to a decaying-oscillating behavior of the highest occupied and lowest unoccupied molecular orbital gap in armchair tubes as a function of length. For zigzag tubes the inclusion of curvature induces the conversion of an extended state at nonbonding energy to an edge state. In addition the transmission coefficient of zigzag and armchair tubes with featureless leads is analytically obtained. The existence of a transmission peak at the Fermi level that decays exponentially with nanotube length for zigzag tubes is explained.