A problem of screening of electron-electron interaction by LO phonons is investigated for bound two-electron systems in bulk semiconductors and semiconductor quantum dots. We consider a D − centre and a two-electron quantum dot and obtain the effective LO-phonon-induced interaction between the electrons, i.e., V eff (r 12) ∼ e 2 /[ε eff (r 12)r 12 ], where r 12 is the interelectron distance and ε eff (r 12) is the effective phonon dielectric function. The calculated phonon dielectric function rapidly increases for small r 12 starting from the high-frequency dielectric constant, ε ∞ , and reaches some constant value,ε, at relatively small interelectron distances. We have found that-in most casesε is less than the static dielectric constant, ε s. Only in the weakly ionic compounds, like GaAs,ε ε s. We argue that-in the bound few-electron systems-ε better approximates the average LO-phonon-induced screening than the commonly used ε s. We have also shown that the coupling with LO phonons leads to the increase of the binding energy of the two-electron system confined in the quantum dot.

Exchange interaction has been studied for electrons in coupled quantum dots (QD's) by a configuration interaction method using confinement potentials with different profiles. The confinement potential has been parametrized by a two-centre power-exponential function, which allows us to investigate various types of QD's described by either soft or hard potentials of different range. For the soft (Gaussian) confinement potential the exchange energy decreases with increasing interdot distance due to the decreasing interdot tunnelling. For the hard (rectangular-like) confinement potential we have found a non-monotonic behaviour of the exchange interaction as a function of distance between the confinement potential centres. In this case, the exchange interaction energy exhibits a pronounced maximum for the confinement potential profile which corresponds to the nanostructure composed of the small inner QD with a deep potential well embedded in the large outer QD with a shallow potential well. This effect results from the strong localization of electrons in the inner QD, which leads to the large singlet-triplet splitting. Implications of this finding for quantum logic operations have been discussed.

The effect of an external electric field on the exchange interaction has been studied by an exact diagonalization method for two electrons in laterally coupled quantum dots (QDs). We have performed a systematic study of several nanodevices that contain two gate-defined QDs with different shapes and sizes located between source and drain contacts. The confinement potential is modeled by two potential wells with a variable range and softness. In all the considered nanodevices, the overall dependence of exchange energy J on electric field F is similar, i.e. for low fields J increases with increasing F, while for intermediate fields J reaches a maximum and then abruptly falls to zero if F exceeds a certain critical value. However, the J(F) dependence also shows certain characteristic properties that depend on the nanodevice geometry. We have found that the low- and intermediate-field behavior can be accurately parameterized by a linear function J(F) = αF+β, where α is independent of the nanodevice geometry and softness of the confinement potential. We have shown that the linear J(F) relation appears only if the tunnel coupling between the QDs is weak, i.e. the interdot separation is sufficiently large. This relation becomes nonlinear for the strong interdot coupling. For specific nanodevices we have found that the J(F) dependence exhibits a plateau in a broad electric-field regime. The properties of the exchange energy found in the present paper can be applied to all electrical manipulation of electron spin qubits.

The effect of external electric field on exchange interaction has been studied by a configuration interaction method for electrons localized in double quantum dots. We model the confinement potential by the twocenter power‐exponential function, with different range and “softness”, which allows us to investigate various types of quantum dots. We have found that – for quantum dots separated by a sufficiently thick barrier – the exchange energy rapidly increases if the electric field increases, for intermediate electric field reaches a maximum, and decreases to zero at high electric fields. We have discussed the physical reasons of this nonmonotonic dependence. The present results show that the exchange coupling between the electrons in quantum dots can be tuned by applying the external electric field (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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