Localization of magnetic and electronic excitations in nanotubes with line defects

A matrix Green's function formalism is employed to study the excitations in long nanotubes where the dynamics are governed by nearest-neighbor interactions between atoms. Examples of the excitations, which can be characterized in terms of the tube circumference and a one-dimensional wave number along the length, include ferromagnetic spin waves in a Heisenberg exchange model and electronic modes in a tight-binding model with hopping. It is assumed that the system is a single-walled nanotube of negligible thickness and that the atoms are arranged on a simple square lattice. Defects in the form of substitutional impurity atoms are introduced to study localized modes as well as the propagating modes of the pure (host) material. The impurities have the form of one or more line defects parallel to the nanotube axis. The derived Green's functions provide a description of the frequencies of the discrete modes of the system and their spectral intensities. Numerical examples are presented for different mode types (magnetic and electronic), nanotube diameters and arrangements of impurity lines.