Singlet-triplet splitting, correlation, and entanglement of two electrons in quantum dot molecules

摘要

Starting with an accurate pseudopotential description of the single-particle states, and following by configuration-interaction treatment of correlated electrons in vertically coupled, self-assembled InAs/GaAs quantum dot molecules, we show how simpler, popularly practiced approximations, depict the basic physical characteristics including the singlet-triplet splitting, degree of entanglement (DOE), and correlation. The mean-field-like single-configuration approaches such as Hartree-Fock and local spin density, lacking correlation, incorrectly identify the ground-state symmetry and give inaccurate values for the singlet-triplet splitting and the DOE. The Hubbard model gives qualitatively correct results for the ground-state symmetry and singlet-triplet splitting, but produces significant errors in the DOE because it ignores the fact that the strain is asymmetric even if the dots within a molecule are identical. Finally, the Heisenberg model gives qualitatively correct ground-state symmetry and singlet-triplet splitting only for rather large interdot separations, but it greatly overestimates the DOE as a consequence of ignoring the electron double occupancy effect.