Reconsideration of the spin-orbit interaction for an electron confined in a quasi-two-dimensional quantum dot: II. Bulkiness and in-plane spin-orbit coupling

We solve the Pauli equation for the quasi-two-dimensional (2D) quantum dot (QD) system numerically by employing the finite difference technique, and reconsider how bulkiness changes the electronic structure through the spin-orbit (SO) interaction. By decomposing the internal SO coupling induced by the confinement potential into the out-of-plane and in-plane components, we demonstrate that the in-plane SO coupling produces the characteristic electronic structure having the opposite spin hybridization. The second-order perturbation approach reveals that this in-plane SO coupling has a function similar to that of Rashba SO coupling and produces the symmetry-broken spin distribution via the interstate interference. We further determine the spin precession by the internal SO coupling and investigate the optimal spin polarization to reduce the spin "fluctuation" effectively.