Augmented cylindrical wave method in the theory of electronic structure of quantum nanowires

Abstract

A computational method for the band structure of nanowires having approximately cylindrical symmetry is developed. The effective one‐electron potential is supposed to have spherical symmetry in the region of the atomic centres and is assumed to be constant in the interstitial region. The corresponding electronic density is supposed to be localised inside the region of cylindrical shape. The base wave functions are obtained by sewing together solutions of the Schrödinger equation for an electron in the empty cylinder (cylindrical waves) with spherically symmetrical solutions for the muffin‐tin spheres. Under the condition of the continuity of the base functions and their first derivatives overlap integrals and Hamiltonian matrix elements are obtained. Dispersion curves and electronic densities of states for chains of transition metals and those of nanowires from metals from K to Zn are calculated.

Linear augmented cylindrical wave method and its applications to nanotubes electronic structure

“…Correspondingly, in the LACW method, the motion of electrons in the space between MT spheres is limited by two cylindrical barriers impenetrable for electrons: the external barrier of radius a and the internal barrier of radius b which are chosen so that the region confined by these barriers accommodates a significant portion of the electron density of the system under consideration. Such a potential is referred to as a cylindrical MT potential [23][24][25].…”

“…Note, that the LACW approach is applicable not only to the carbon nanotubes. For example, the inner cavity of the carbon tubules can be filled with a variety of substances including the transition metals, and we applied the LACW method to predict the bands of the tubules doped with 3d-metals [23][24][25]. 4 show the data for infinite Cu chain and intercalated Cu@C(5,5) tubule for the case when the periodicity of Cu chain coincides with that for carbon system.…”

Spin-Orbit Gaps in Armchair Nanotubes Calculated Using the Linear Augmented Cylindrical Wave Method

“…The sum H 0 = p 2 /(2m) + V is the nonrelativistic Hamiltonian which was previously used for the LACW band structure studies [18][19][20][21][22][23]. The third term of the Hamiltonian (1) is the familiar spin-orbit coupling term, which may split the degenerate levels and cause mixing of levels thus altering the band picture.…”

“…Use of the relations (18)(19)(20) together with the ortogonality and normalization of the spin functions α and β and of the spherical harmonics, allows the angular integration to be performed analytically to give finally 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 1 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 2 1 1 1 1 2 2 …”

Description of band structures of armchair nanotubes using the symmetry‐adapted linear augmented cylindrical wave method

“…The LACW method [6][7][8][9][10][11] is just a reformulation of the linear augmented plane wave theory for cylindrical multiatomic systems [12,13]. The metallic armchair tubes are of interest as possible components in nanoscale electronic circuits.…”