The Spin–Orbit Mechanism of Electron Pairing in Quantum Wires

Abstract

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.

Bound Electron Pairs Formed by the Spin–Orbit Interaction in 2D Gated Structures

“…On the contrary, in 1D systems, PSOI is created only by a normal component of the field, which arises when the axial symmetry of the system is broken, for example, by a proximate gate. In this case, PSOI originates from image charges induced by the interacting electrons at the gate and also leads to BEP formation …”

“…For a pair of electrons, its position is given bywhere stands for the gate field of Equation normalized according to , with . In 1D quantum wires, the BEPs always lie below . This is not, generally speaking, the case in a 2D system.…”

“…Thus, the pair interaction we consider here is attractive on a small scale and repulsive on the large distance. The bound electron pairs (BEPs) formed as a result of this interaction [4][5][6] are drastically different from other composite particles, which are currently widely studied in bulk materials, [7,8] low-dimensional systems, [9][10][11][12][13] and even for cold atoms in optical lattice. [14] Another feature of the PSOI is that it depends on the configuration of the Coulomb field which acts between electrons and can be controlled by a gate in low-dimensional systems.…”

“…In this case, PSOI originates from image charges induced by the interacting electrons at the gate [15] and also leads to BEP formation. [4] The spectrum of the BEPs together with their spin structure is quite different, depending on whether the PSOI is produced solely by the in-plane field or by the normal electric field. Despite the difference in the electric field configuration in both cases, one can still classify the BEPs according to the nature of the electron motion, which produces the PSOI, to arrive at two distinct types of BEPs.…”

“…In 1D quantum wires, the BEPs always lie below ε c . [4] This is not, generally speaking, the case in a 2D system. Increasing F g lowers ε c , keeping ε 0 intact, so eventually the energy level ε 0 gets into the conduction band.…”