  We solve a two-body problem for electrons in a one-dimensional system to show
that two-electron bound states can arise as a result of the
image-potential-induced spin-orbit interaction (iSOI). The iSOI contributes an
attractive component to the electron-electron interaction Hamiltonian that
competes with the Coulomb repulsion and overcomes it under certain conditions.
We find that there exist two distinct types of two-electron bound states,
depending on the type of the motion that forms the iSOI: the relative motion or
the motion of the electron pair as a whole. The binding energy lies in the meV
range for realistic material parameters and is tunable by the gate potential.
