The Spin–Orbit Mechanism of Electron Pairing in Quantum Wires

A two-body problem for electrons in a one-dimensional system is solved here 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. It is found 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.