  Metallic nanowires can exhibit fascinating physical properties. These unique
properties often originate primarily from the quantum confinement of free
electrons in a potential well, while electron-electron interactions do not play
a decisive role. A recent experimental study shows that self-assembled Ir
nanowires grown on Ge(001) surface have a strong length preference: the
nanowire lengths are an integer multiple of 4.8 nm. In this paper, a free
electron-gas model for geometries corresponding to the nanowires is used to
analyze the selection of these preferred or magic lengths. The model shows that
the inclusion of even numbers of free electrons in an Ir nanowire corresponds
to these magic lengths once an electron spillage effect is taken into account.
The model also shows that the stability of the nanowire diminishes with its
increasing length, and consequently suggests why no long nanowires are observed
in experiments. It is also shown that applying generic results for quantum size
effects in a nanofilm geometry is not adequate to accurately describe the
length selection in the rather different nanowire geometry, where the
transverse dimensions smaller than the electron Fermi wavelength. Finally, the
monatomic Au chain growth on Ge(001) surface is also analyzed. In contrast to
Ir nanowires, the model shows that the stability of an Au chain strongly
depends on its electron spillage.
