Spin-orbit-driven electron pairing in two dimensions

We show that the spin-orbit interaction (SOI) arising due to the in-plane electric field of the Coulomb repulsion between electrons in a two-dimensional quantum well produces an attractive component in the pair interaction Hamiltonian that depends on the spins and momenta of electrons. If the Rashba SOI constant of the material is high enough, the attractive component overcomes the Coulomb repulsion and the centrifugal barrier, which leads to the formation of the two-electron bound states. There are two distinct types of two-electron bound states. The relative bound states are formed by the electrons orbiting around their common barycenter. They have a triplet spin structure and are independent of the center-of-mass momentum. In contrast, the convective bound states are formed because of the center-of-mass motion, which couples the electrons with opposite spins. The binding energy in the meV range is attainable for realistic conditions.

Figure 1

The effective binding potential for the relative bound states with $l=1$ and separate contributions from the centrifugal potential, direct Coulomb $e-e$ interaction, and SOI.

Figure 2

The radial part of the wave function of the relative bound state (up to the normalization constant) together with the effective binding potential for $d=0.25a_B$.

Figure 3

The dependence of ${\lambda }_m\left(\mathcal{A}\right)$ on $\mathcal{A}$ for several values of $m$.

Figure 4

The polar diagram $\left(f_{\uparrow \downarrow }^{\left(0\right)}\left(\varphi \right),\varphi \right)$ for several values of $\mathcal{A}$.

Figure 5

The system energy levels (solid lines) and the kinetic energy of the center of mass (dashed line) vs $\mathcal{A}$ for $d=0.25a_B$.

Figure 6

The ground-state energy (solid line) and the kinetic energy of the center of mass (dashed line) vs $\mathcal{A}$ for $d=0.2a_B$.

Figure 7

The spinor components of the convective state wave function for $d=0.25a_B$ and $\mathcal{A}=5$ as functions of relative coordinates. Two surfaces are moved apart vertically by $\delta =\pm 0.02$ for better visual perception. The arrow shows the direction of vector $\mathbf{K}$ (along the $y$ axis).

Figure 8

The first zero $x_1$ of $\mathcal{K}{}_{i\mu }\left(x\right)$ as a function of $\mu$.