  Domain walls, arising from the spontaneous breaking of a discrete symmetry,
can be coupled to charge carriers. In much the same way as the Witten model for
superconducting cosmic string, an investigation is made here in the case of
$U(1)\times Z_2 \to U(1)$, where a bosonic charge carrier is directly coupled
to the wall-forming Higgs field. All internal quantities, such as the energy
per unit surface and the surface current, are calculated numerically to provide
the first complete analysis of the internal structure of a surface
current-carrying domain wall.
