  We simulate the electron transport in vertical bi-layer nanowire which can be
fabricated in molecular beam epitaxy process with lateral confinement potential
formed by means of cleaved overgrowth or surface oxidization methods giving
rectangular and smooth side confinement, respectively. In calculations we take
into account interaction between charge carriers using DFT within local spin
density approximation. If magnetic field is perpendicular to the wire axis,
pseudogaps are opened in energy dispersion relation E(k) what in conjunction
with spin Zeeman shift of spin-up and spin-down subbands allows for quite high
spin polarization of conductance. We find that in nanowire with rectangular
lateral confinement potential, electron density has two maximums localized at
wire edges in each layers. This modificates strongly all magnetosubbands giving
up to four energy minimums in lowest subband and considerably diminishes widths
of pseudogaps what translates into low maximal spin polarization of
conductance, not exceeding $40\%$. This drawback is absent in wire with smooth
lateral confinement. However, in order to gain a large spin polarization
simultaneous tuning of magnetic field as well as the Fermi energies in both
layers of nanowire are required.
