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Tunable exchange interaction in coupled quantum dots

Jihan Kim

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Exchange energies and charge densities for few electrons in electrically tunable quantum dot (QD) systems are investigated by using the variational Monte Carlo (VMC) method in the presence of magnetic fields. For N = 2 electrons in double QD, the singlet Coulomb energy decreases in magnetic fields as a consequence of magnetic localization in both strongly and weakly coupled QDs. However, the triplet Coulomb energy reaches a maximum value at intermediate magnetic fields before decreasing. We observe good agreement between the results for VMC with s-p orbital trial wavefunction and exact diagonalization (ED) method in the exchange energies. For N = 2 electrons in triple quantum dot (TQD), we observe a discontinuity in the J-derivative with detuning voltage ( dJdVT ) in triangular TQDs at B = 0 T as crossing of the eigenenergy levels leads to abrupt spatial symmetry change of the triplet densities (density rotation) and relocalization. For B ≠ 0 T, the angular momentum provided to the electrons quenches this effect. The density rotation is absent in collinear TQD for all magnetic fields as the lowest excited state remains the px state and as such, no change in symmetry is possible. By varying the triangular TQD configuration, we show the discontinuity in ( dJdVT ) persists for top angle between 20° and 70°. For N = 3 electrons in symmetric triangular TQD, the monotonicity of the exchange curve from B = 0 to 4 T remains intact for decoupled QDs but not for coupled QDs. Finally, additional energy for the triangular TQD system is computed for up to N = 3 electrons.

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Exchange energies and charge densities for few electrons in electrically tunable quantum dot (QD) systems are investigated by using the variational Monte Carlo (VMC) method in the presence of magnetic fields. For N = 2 electrons in double QD, the singlet Coulomb energy decreases in magnetic fields as a consequence of magnetic localization in both strongly and weakly coupled QDs. However, the triplet Coulomb energy reaches a maximum value at intermediate magnetic fields before decreasing. We observe good agreement between the results for VMC with s-p orbital trial wavefunction and exact diagonalization (ED) method in the exchange energies. For N = 2 electrons in triple quantum dot (TQD), we observe a discontinuity in the J-derivative with detuning voltage ( dJdVT ) in triangular TQDs at B = 0 T as crossing of the eigenenergy levels leads to abrupt spatial symmetry change of the triplet densities (density rotation) and relocalization. For B ≠ 0 T, the angular momentum provided to the electrons quenches this effect. The density rotation is absent in collinear TQD for all magnetic fields as the lowest excited state remains the px state and as such, no change in symmetry is possible. By varying the triangular TQD configuration, we show the discontinuity in ( dJdVT ) persists for top angle between 20° and 70°. For N = 3 electrons in symmetric triangular TQD, the monotonicity of the exchange curve from B = 0 to 4 T remains intact for decoupled QDs but not for coupled QDs. Finally, additional energy for the triangular TQD system is computed for up to N = 3 electrons.
Exchange interaction has been studied for electrons in coupled quantum dots (QDs) 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 QDs described by either soft or hard potentials of different ranges. 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 exchange interaction in a singlet-triplet qubit defined by two-electron states in the double-quantum-dot system (``two-electron singlet-triplet qubit'') typically varies monotonically with the exchange interaction and thus carries no sweet spot. Here we study a singlet-triplet qubit defined by four-electron states in the double-quantum-dot system (``four-electron singlet-triplet qubit''). We demonstrate, using configuration-interaction calculations, that in the four-electron singlet-triplet qubit the exchange energy as a function of detuning can be nonmonotonic, suggesting existence of sweet spots. We further show that the tuning of the sweet spot and the corresponding exchange energy by perpendicular magnetic field can be related to the variation of orbital splitting. Our results suggest that a singlet-triplet qubit with more than two electrons can have advantages in the realization of quantum computing.
We determine the spin-exchange coupling J between two electrons located in two vertically tunnel-coupled quantum dots, and its variation when magnetic (B) and electric (E) fields (both in-plane and perpendicular) are applied. We predict a strong decrease of J as the in-plane B field is increased, mainly due to orbital compression. Combined with the Zeeman splitting, this leads to a singlet-triplet crossing, which can be observed as a pronounced jump in the magnetization at in-plane fields of a few T, and perpendicular fields of the order of 10 T for typical self-assembled dots. We use harmonic potentials to model the confining of electrons, and calculate the exchange J using the Heitler-London and Hund-Mulliken techniques, including the long-range Coulomb interaction. With our results we provide experimental criteria for the distinction of singlet and triplet states, and therefore for microscopic spin measurements. In the case where dots of different sizes are coupled, we present a simple method to switch the spin coupling on and off with exponential sensitivity using an in-plane electric field. Switching the spin coupling is essential for quantum computation using electronic spins as qubits.
We have used a hybrid vertical-lateral double quantum dot to study the excitation energy spectrum for one- and two-electron states, which are effectively formed on top of a certain core shell. We have observed bonding and antibonding states, and exchange coupled singlet and triplet states for the one- and two-electron states, respectively, and derived the interdot tunnel coupling and exchange coupling energies for various parameters of interdot level detuning, central gate voltage and magnetic field. The obtained exchange coupling energy is consistently reproduced by calculation using the Hund-Mulliken method.
Recent works indicate that coupled quantum dots (QD) are promising nanostructures for realizing quantum gates that are the basic elements of a quantum computer. In QDs, fundamental quantum logic operations can be achieved in a quantum gate by controlling the entanglement between two electron spins by means of external electric and magnetic fields. This chapter describes the computational approach used to solve the many-body Schrodinger equation. It provides results of the simulations for both the strongly coupled and weakly coupled QDs and analyzes the important differences between the two cases. The utilization of simple trial wavefunctions in VMC have lead to good agreement with the ED method, when electrons are decoupled, which validates two-level approaches such as the Heitler-London approximation in weakly coupled QDs.
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.