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

Abstract

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 inter-dot separations, but it greatly overestimates the DOE as a consequence of ignoring the electron double occupancy effect.

Electronic structures of(In,Ga)As∕GaAsquantum dot molecules made of dots with dissimilar sizes

“…We have demonstrated 8,9 that dot-localized orbitals can be a useful tool to analyze the QDM physics, including the electron double occupation, and two-electron entanglement.…”

“…The energy levels of M αβ are similar to those of M γγ , in the following way: (i) The order of the CI levels is unchanged, particularly the ground states are still the singlet states 1 Σ localized on the same dots. 8,9 The energy difference be-…”

“…8,9 We have studied electron localization, double occupation rate and two-electron entanglement using a new formula for measuring the degree of entanglement formula for two indistinguishable fermions. We found that even geometrically identical dots in the QDMs lead to electronic asymmetry due to the strain effects.…”

Building semiconductor nanostructures atom by atom

“…In single dots, the lack of inversion symmetry of the lattice may lead to a removal of single-particle degeneracies, and in particular a splitting of the p shell states [18]. As we shall show later on, in the case of dot molecules the lack of inversion symmetry of the lattice introduces an overall asymmetry of the system even if the dots composing it are identical [19,20]. In order to bring the dots into resonance, the structural asymmetry has to be compensated, e.g., by applying an external electric field [21].…”

“…These approaches can be divided into two groups. In the empirical pseudopotential methods [19,22] one attempts to derive the basis orbitals by assuming that the nucleus and all core electrons localized on each atom contribute to a singleparticle pseudopotential in its vicinity. In this work, however, we focus on the atomistic tight-binding approach, in which the atomic basis is never completely defined, but the Hamiltonian matrix elements describing the coupling of neighboring atoms are treated as fitting parameters.…”