Reconsideration of relativistic corrections for an electron confined in a two-dimensional quantum dot: I. Spin-orbit coupling and Rashba effect

By implementing the relativistic corrections of Pauli's spin-orbit (SO) coupling, Darwin's correction, and mass-velocity (MV) interaction, we computationally study the electronic structure of an electron confined in a two-dimensional (2D) quantum dot (QD), and discuss the influence of these relativistic terms. We further study the influence of the Rashba effect on the electronic structure. In the typical semiconductor QD system, the Rashba effect causes a sizeable shift to the energy eigenstates on the order of a milli-electron volt whereas the other relativistic corrections of the internal SO interaction, MV coupling, and Darwin term amount to a shift in energy eigenstates on the order of less than a micro-electron volt, and are largely negligible. The Rashba coupling hybridizes the opposite spin state, and the second-order perturbation approach reveals that this hybridization causes the interstate interference and a curious distribution appears in the spin density in the degenerated state.