Linear augmented cylindrical wave method for nanotubes electronic structure

Abstract

In this review paper, the main ideas and results of application of the linearized augmented cylindrical wave (LACW) method for the electron properties of the single-walled, double-walled, embedded, and intercalated nanotubes are summarized. We start with the simplest case of the achiral single-walled (n, 0) and (n, n) tubules having small translational unit cells. Then, the electron properties of chiral (n, m) nanotubes having very large translational cells are discussed with account of tubules possessing rotational and screw symmetries. Based on the LACW and Green's function techniques, the ab initio numerical approach to calculating the electron local densities of states of the substitutional impurities in the nanotubes is presented. The relativistic version of LACW theory is described and applied to calculating the effects of spin-orbit coupling on π-bands of the cumulenic (C)n and polyynic (C2)n carbynes and armchair tubules. The approach of the cylindrical waves applied for the description of nanotubes permits to reproduce their geometry in an explicit form that offers the great advantages.