  We report on a theoretical study of the electronic structures of InSb and
GaSb nanowires oriented along the [001] and [111] crystallographic directions.
The nanowires are described by atomistic, spin-orbit inteaction included,
tight-binding models, and the band structures and the wave functions of the
nanowires are calculated by means of a Lanczos iteration algorithm. For the
[001]-oriented InSb and GaSb nanowires, the systems with both square and
rectangular cross sections are considered. Here, it is found that all the
energy bands are double degenerate. Furthermore, although the lowest conduction
bands in these nanowires show good parabolic dispersions, the top valence bands
show rich and complex structures. In particular, the topmost valence bands of
these nanowires with a square cross section show a double maximum structure. In
the nanowires with a rectangular cross section, this double maximum structure
is suppressed and top valence bands gradually develop into parabolic bands as
the aspect ratio of the cross section is increased. For the [111]-oriented InSb
and GaSb nanowires, the systems with hexagonal cross sections are considered.
It is found that all the bands at the \Gamma-point are again double degenerate.
However, some of them will split into non-degenerate bands when the wave vector
moves away from the \Gamma-point. Furthermore, although the lowest conduction
bands again show good parabolic dispersions, the topmost valence bands do not
show the double maximum structure but, instead, a single maximum structure with
its maximum at a wave vector slightly away from the \Gamma-point. We also
investigate the effects of quantum confinement on the band structures of the
[001]- and [111]-oriented InSb and GaSb nanowires and present an empirical
formula for the description of quantization energies of the band edge states in
the nanowires.
