  We study the electron transmission through the domain boundary on bilayer
graphene separating AB and BA stacking regions. Using the effective continuum
model, we calculate the electron transmission probability as a function of the
electron energy and the incident angle, for several specific boundary
structures. The transmission strongly depends on the crystallographic direction
of the boundary and also on the atomic configuration inside. At the low energy,
the boundary is either insulating or highly transparent depending on the
structure. In insulating cases, the transmission sharply rises when the Fermi
energy is increased to a certain level, suggesting that the electric current
through the boundary can be controlled by the field effect. The boundary
parallel to the zigzag direction generally have different transmission
properties between the two different valleys, and this enables to generate the
valley polarized current in a certain configuration. We show that those
characteristic features can be qualitatively explained by the transverse
momentum conservation in the position-dependent band structure in the
intermediate region.
