The spin-orbit mechanism of electron pairing in quantum wires

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.