  We report on a theoretical study of the electronic structures of freestanding
nanowires made from narrow band gap semiconductors GaSb, InSb and InAs. The
nanowires are described by the eight-band k.p Hamiltonians and the band
structures are computed by means of the finite element method in a mixture
basis consisting of linear triangular elements inside the nanowires and
constrained Hermite triangular elements near the boundaries. The nanowires with
two crystallographic orientations, namely the [001] and [111] orientations, and
with different cross-sectional shapes are considered. For each orientation, the
nanowires of the three narrow band gap semiconductors are found to show
qualitatively similar characteristics in the band structures. However, the
nanowires oriented along the two different crystallographic directions are
found to show different characteristics in the valence bands. In particular, it
is found that all the conduction bands show simple, good parabolic dispersions
in both the [001]- and [111]-oriented nanowires, while the top valence bands
show double-maximum structures in the [001]-oriented nanowires, but
single-maximum structures in the [111]-oriented nanowires. The wave functions
and spinor distributions of the band states in these nanowires are also
calculated. It is found that significant mixtures of electron and hole states
appear in the bands of these narrow band gap semiconductor nanowires. The wave
functions exhibit very different distribution patterns in the nanowires
oriented along the [001] direction and the nanowires oriented along the [111]
direction. It is also shown that single-band effective mass theory could not
reproduce all the band state wave functions presented in this work.
