Two-electron Quantum Dot Research Articles

Quantitative modeling of spin relaxation in quantum dots

We use numerically exact diagonalization to calculate the spin-orbit and phonon-induced triplet-singlet relaxation rate in a two-electron quantum dot exposed to a tilted magnetic field. Our scheme includes a three-dimensional description of the quantum dot, the Rashba and the linear and cubic Dresselhaus spin-orbit coupling, the ellipticity of the quantum dot, and the full angular description of the magnetic field. We are able to find reasonable agreement with the experimental results of Meunier et al. [Phys. Rev. Lett. 98, 126601 (2007)] in terms of the singlet-triplet energy splitting and the spin relaxation rate, respectively. We analyze in detail the effects of the spin-orbit factors, magnetic-field angles, and the dimensionality, and discuss the origins of the remaining deviations from the experimental data.

Spin–flip relaxation in a two-electron quantum dot with spin–phonon coupling

We study the spin–flip process from the first excited state to the ground state due to the spin–phonon coupling in a two-electron quantum dot in the presence of a magnetic field. We give several possible relaxation channels before and after the crossing of the Zeeman sublevels. Our results show that the Coulomb interactions between the electrons of different channels play quite different roles and thus inducing different spin relaxation behaviors.

Semiclassical model for the dephasing of a two-electron spin qubit coupled to a coherently evolving nuclear spin bath

We study electron spin decoherence in a two-electron double quantum dot due to the hyperfine interaction, under spin-echo conditions as studied in recent experiments. We develop a semi-classical model for the interaction between the electron and nuclear spins, in which the time-dependent Overhauser fields induced by the nuclear spins are treated as classical vector variables. Comparison of the model with experimentally-obtained echo signals allows us to quantify the contributions of various processes such as coherent Larmor precession and spin diffusion to the nuclear spin evolution.

Electric field effects on the intersubband optical absorptions and refractive index in double-electron quantum dots

The linear and nonlinear optical properties such as optical absorption and refractive index change associated with intersubband transitions in a two-electron quantum dot (QD) in the presence of an external electric field have been investigated theoretically by using the perturbation method. The exchange force, which is a strictly quantum mechanical phenomenon, has also been considered. Numerical results on typical GaAs/AlGaAs materials show that an increase of the electric field decreases the oscillator strengths, the peak positions of absorption coefficients as well as the refractive index changes. Additionally, an increase of the confinement frequency (dot size) increases (decreases) the absorption coefficients but does not significantly affect the refractive index changes. It is also observed that the intensity of the illumination and the relaxation time have drastic effects on nonlinear optical properties. Finally, we note that the optical absorption coefficients and refractive index changes of two electrons are about five times higher than that of a one-electron QD.

Tuning of anisotropy in two-electron quantum dots by spin-orbit interactions

We investigate the influence of the spin-orbit interactions (SOIs) on the electron distribution and the optical absorption of a two-electron quantum dot. It is shown that the interplay between the SOIs makes the two-electron quantum dot behave like two laterally coupled quantum dots and the anisotropic distribution can be rotated from [110] to [11®0] by reversing the direction of the perpendicular electric field and detect it through the optical absorption spectrum.

Tuning of the spin-orbit interaction in a quantum dot by an in-plane magnetic field

Using an exact diagonalization approach we show that one- and two-electron InAs quantum dots exhibit avoided crossing in the energy spectra that are induced by the spin-orbit coupling in the presence of an in-plane external magnetic field. The width of the avoided crossings depends strongly on the orientation of the magnetic field which reveals the intrinsic anisotropy of the spin-orbit coupling interactions. We find that for specific orientations of the magnetic field avoided crossings vanish. Value of this orientation can be used to extract the ratio of the strength of Rashba and Dresselhaus interactions. The spin-orbit anisotropy effects for various geometries and orientations of the confinement potential are discussed. Our analysis explains the physics behind the recent measurements performed on a gated self-assembled quantum dot [S. Takahashi et al. Phys. Rev. Lett. 104, 246801 (2010)].

Polaron effect on the optical absorption and refractive index of an exciton in quantum dots

We have studied the optical absorption of an exciton and its refractive index in a disc-like quantum dot, taking into account of the confined longitudinal optical (LO) phonons. Calculations are performed in the framework of the effective-mass approximation using the compact density-matrix approach. With typical semiconducting GaAs materials, the linear, third-order nonlinear, total optical absorption coefficients and refractive index changes with and without considering the exciton–phonon interaction have been examined. By comparing the polaron effect of the two-electron quantum dot, it is found that the corrections due to the LO phonons on the optical absorption and refractive index are very important and cannot be ignored.

Asymptotic iteration study of a two-electron GaAs quantum dot

Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic gallium arsenide (GaAs) quantum dot (QD) and subjected to an external uniform magnetic field of arbitrary strength have been calculated within the framework of the asymptotic iteration method. Comparing the present results with exact numerical values and with the results calculated by earlier workers, it is found that asymptotically, this method gives accurate results valid for the whole range of both spatial confinement length and the strength of the magnetic field. The present method yields a significant improvement over the Hartree, Hartree–Fock and exact diagonalization treatments, and its results are in agreement with those of a Monte Carlo analysis. Therefore, this approach and its results proposed here would be very helpful in discussing the size-dependent properties of low-lying energy of any QD with two or more electrons.

Spin dynamics at the singlet–triplet crossings in a double quantum dot

We simulate the control of the spin states in a two-electron double quantum dot when an external detuning potential is used to pass the system through an anticrossing. The hyperfine coupling of the electron spins with the surrounding nuclei causes not only anticrossing of the spin states but also decoherence of the spin states. We calculate numerically the singlet–triplet decoherence for different detuning values and find good agreement with the experimental measurement results for a similar setup. We predict an interference effect due to the coupling of the T0 and T+ states.

Linear and nonlinear optical absorption coefficients and refractive index changes in a two-electron quantum dot

Analytical expressions of the optical absorption coefficients and refractive index changes in a two-electron quantum dot with oscillating and linear confining terms are obtained by using compact-density matrix approach and exact analytical method. Numerical results on typical GaAs/AlGaAs materials show that, an increase of the confinements blueshifts the peak positions of absorption coefficients and refractive index changes. Additionally, an increase of the optical intensity and relaxation time considerably changes the absorption coefficients as well as the refractive index changes.

Approximation of the entanglement in quantum dot chains using Hubbard models

We investigate the Hubbard model, and the extended Hubbard model with and without correlated hopping, as an approximation to the average single-site (or local) entanglement of two-electron one-dimensional quantum dot chains with long range interactions. We focus on the effect of the chain length on the approximation accuracy. We also consider the particle-particle spatial entanglement of the three Hubbard models using the technique of Ref. [3] and compare the accuracy of this approximation to the numerically exact results of the nanostructure system.

Polaron effects on linear and nonlinear optical properties of a two-electron quantum dot

The linear and nonlinear optical properties of parabolic quantum dots in which two electrons interact with each other through both coulomb repulsion and longitudinal-optical phonon are studied by using the matrix diagonalization method. With typical semiconducting GaAs-based materials, the linear, third-order nonlinear, total optical absorption coefficients and the optical refractive index have been examined. The effects of different electron–phonon coupling strengths on the linear and nonlinear optical properties are also predicted.

Correlation and Entanglement in Elliptically Deformed Two-Electron Quantum Dots

We study quantum correlation in a two-dimensional system of two Coulombically interacting electrons trapped in an anisotropic harmonic potential in dependence on the interaction strength. The linear entropy and von Neumann entropy that measure the entanglement between the electrons are compared with the correlation energy and the statistical correlation coefficient. We observe that the entanglement properties are dramatically influenced by the anisotropy of the confining potential.

Exchange-correlation potential with a proper long-range behavior for harmonically confined electron droplets

The exchange-correlation potentials stemming from the local-density approximation and several generalized-gradient approximations are known to have incorrect asymptotic decay. This failure is independent of the dimensionality but so far the problem has been corrected---within the mentioned approximations---only in three dimensions. Here we provide a cured exchange-correlation potential for two-dimensional harmonically confined systems that cover a wide range of applications in quantum Hall and semiconductor physics, especially in quantum-dot modeling. The given potential is a generalized-gradient approximation and we demonstrate that it agrees very well with the analytic result of a two-electron quantum dot in the asymptotic regime, and yields plausible results for larger two-dimensional systems.

EFFECTS OF HYDROSTATIC PRESSURE AND POLARONIC EFFECTS ON THE CORRELATION ENERGIES IN A SPHERICAL QUANTUM DOT

The correlation energies in a singlet and in a triplet state of a two-electron quantum dot in a finite barrier square well potential are computed. Closed analytical expressions are obtained in the perturbation method. Effects of band non-parabolicity and polaronic correction are included. Effects of hydrostatic pressure on the correlation energies are computed. Our results show that (i) the correlation energies in the triplet state are negative, reflecting the exchange interaction, (ii) both the singlet and triplet state correlation energies approach zero as the dot size approaches infinity, (iii) while the band non-parabolicity and the polaronic effects are not significant in the estimation of correlation energies, they however decrease the total confined energies to a maximum of 43% in the triplet state, and (iv) the hydrostatic pressure affects the confined energies appreciably for narrow dots only. The interesting cross-over behavior of the triplet and the singlet state energies at a particular dot radius is explained physically.

An orbital entanglement in two-electron quantum dots in a magnetic field

We consider a simple model for two-electron quantum dots (QDs) in the perpendicular magnetic field. With the aid of this model we study the degree of the orbital entanglement as a function of the magnetic field strength and the QD shape. We found that the circular QD exhibits no entanglement in the magnetic field. Although the entanglement increases with the increase of the QD deformation at a fixed value of the magnetic field, it approaches the constant value at the fixed deformation with the increase of the magnetic field.

Charge dynamics in two-electron quantum dots

We investigate charge dynamics in a two-electron double quantum dot. The quantum dot is manipulated by using a time-dependent external voltage that induces charge oscillations between the dots. We study the dependence of the charge dynamics on the external magnetic field and on the periodicity of the external potential. We find that for suitable parameter values, it is possible to induce both one-electron and two-electron oscillations between the dots.

The scaling of the density of states in systems with resonance states

Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. We present numerical evidence about the critical behavior of the density of states (DOS) in the region where there are resonances. The critical behavior is signaled by a strong dependence of some features of the DOS on the basis-set size used to calculate it. The resonance energy and lifetime are obtained using the scaling properties of the DOS.

Spin-orbit coupling and anisotropic exchange in two-electron double quantum dots

The influence of the spin-orbit interactions on the energy spectrum of two-electron laterally coupled quantum dots is investigated. The effective Hamiltonian for a spin qubit pair proposed in Baruffa et al. [Phys. Rev. Lett. 104, 126401 (2010)] is confronted with exact numerical results in single and double quantum dots in zero and finite magnetic field. The anisotropic exchange Hamiltonian is found quantitatively reliable in double dots in general. There are two findings of particular practical importance: (i) the model stays valid even for maximal possible interdot coupling (a single dot), due to the absence of a coupling to the nearest excited level, a fact following from the dot symmetry. (ii) In a weak-coupling regime, the Heitler-London approximation gives quantitatively correct anisotropic exchange parameters even in a finite magnetic field, although this method is known to fail for the isotropic exchange. The small discrepancy between the analytical model (which employs the linear Dresselhaus and Bychkov-Rashba spin-orbit terms) and the numerical data for GaAs quantum dots is found to be mostly due to the cubic Dresselhaus term.

Singlet-triplet relaxation in multivalley silicon single quantum dots

We investigate the singlet-triplet relaxation due to the spin-orbit coupling together with the electron-phonon scattering in two-electron multivalley silicon single quantum dots, using the exact diagonalization method and the Fermi golden rule. The electron-electron Coulomb interaction, which is crucial in the electronic structure, is explicitly included. The multivalley effect induced by the interface scattering is also taken into account. We first study the configuration with a magnetic field in the Voigt configuration and identify the relaxation channel of the experimental data by Xiao {\em et al.} [Phys. Rev. Lett. {\bf 104}, 096801 (2010)]. Good agreement with the experiment is obtained. Moreover, we predict a peak in the magnetic-field dependence of the singlet-triplet relaxation rate induced by the anticrossing of the singlet and triplet states. We then work on the system with a magnetic field in the Faraday configuration, where the different values of the valley splitting are discussed. In the case of large valley splitting, we find the transition rates can be effectively manipulated by varying the external magnetic field and the dot size. The intriguing features of the singlet-triplet relaxation in the vicinity of the anticrossing point are analyzed. In the case of small valley splitting, we find that the transition rates are much smaller than those in the case of large valley splitting, resulting from the different configurations of the triplet states.