  Structures and electronic properties of rhombohedral [111] and [110] bismuth
nanowires are calculated with the use of density functional theory. The
formation of an energy band gap from quantum confinement is studied and to
improve estimates for the band gap the GW approximation is applied. The [111]
oriented nanowires require surface bonds to be chemically saturated to avoid
formation of metallic surface states whereas the surface of the [110] nanowires
do not support metallic surface states. It is found that the onset of quantum
confinement in the surface passivated [111] nanowires occurs at larger critical
dimensions than for the [110] nanowires. For the [111] oriented nanowires it is
predicted that a band gap of approximately 0.5 eV can be formed at a diameter
of approximately 6 nm, whereas for the [110] oriented nanowires a diameter of
approximately 3 nm is required to achieve a similar band gap energy. The GW
correction is also applied to estimates of the electron affinity, ionisation
potentials and work functions for both orientations of the nanowires for
various diameters below 5 nm. The magnitude of the energy band gaps that arise
in bismuth at critical dimensions of a few nanometers are of the same order as
for conventional bulk semiconductors.
