Magnetic properties of graphene-like quantum dots doped with magnetic ions

Graphene-like quantum dots (GQDs) doped with magnetic ions are described in accordance with the mixed Ising model. The magnetic properties of this system are discussed within the framework of the effective field theory with correlations. The numerical results produced several types of phase diagrams with different exchange couplings and anisotropies. Certain unique features, such as reentrant phenomena, were found within a particular range of parameters. We concluded that GQDs doped with magnetic ions have the potential to adjust their performance and effectively enlarge the scope of application.     

Planar Dirac electrons in magnetic quantum dots

In this paper, we explore the size- and mass-dependent energy spectra and the electronic correlation of two- and three-electron graphene magnetic quantum dots. It is found that only the magnetic dots with large size can well confine the electrons. For large graphene magnetic dots with massless (ultra-relativity) electrons, the energy level structures of two Dirac electrons and even the ground state spin and angular momentum of three electrons are quite different from those of the usual semiconductor quantum dots. Also we reveal that such differences are not due to the magnetic confinement but originate from the character of the Coulomb interaction of two-component electronic wavefunctions in graphene. We reveal that the increase of the mass leads to both the crossover of the energy spectrum structures from the ultra-relativity to non-relativity ones and the increasing of the crystallization. The results are helpful for the understanding of the mass and size effects and may be useful in controlling the few-electron states in graphene-based nanodevices.     

Interacting electrons in quantum dots

The ground states of N-electron parabolic quantum dots in the presence of a perpendicular magnetic field are investigated. Rigorous lower bounds to the ground-state energies are obtained. It is shown that our lower bounds agree well with the results of exact diagonalization. Analytic results for the lower bounds to the ground-state energies of the quantum dots in a strong magnetic field (known as electron molecule) agree very well with numerically calculated lower bounds.     

Exchange and Coulomb interactions of two electrons in double ellipsoidal quantum dots

The present study seeks to scrutinize the interactions of two electrons on the electronic properties of double ellipsoidal quantum dots (EQD). In this regard, the effective-mass approximation within a perturbation scheme is used and the Coulomb and exchange energies of the two electrons ellipsoidal quantum dot are calculated for GaAs/GaAlAs/AlAs structure. The results showed that the Coulomb and exchange energies depend not only on the thickness of the intermediate layer but also on the ellipticity constant.     

Impurity states of electrons in quantum dots in external magnetic fields

The influence of isolated impurity atoms on the electron energy spectrum in a parabolic quantum dot in quantizing magnetic field is studied. The impurity potential is approximated by a Gaussian separable operator which allows one to obtain the exact solution of the problem. We demonstrate that in the electron energy spectrum there is a set of local levels which are split from the Landau zone boundaries in the upward or downward direction depending on the impurity type. We have calculated the local level positions, the wave functions of electrons in bound states, and the residues of the electron scattering amplitudes by impurity atoms at the poles.     

Electronic structure of quantum dots with two electrons in tilted magnetic fields

The energy levels of a spheroidal quantum dot in tilted magnetic fields are calculated and compared with those for a disk-like dot. The magneto-optical spectrum and the ground state show considerable difference between the two quantum dots. We find that this feature can be understood by considering the magneto-electric hybridization and electron-electron interaction effects on the energy spectrum.     

Correlated electrons in coupled quantum dots and related phenomena

Three topics related to correlated electrons in coupled quantum dots are discussed. The first is quasi-resonance between multi-electron states, which causes hitherto unremarked types of resonant absorption in coupled quantum dots. The second is electron tunneling through a Hubbard gap, which is induced by an increase in the density of electrons in a quantum-dot chain under an overall confining potential. The third is Mott transition in a two-dimensional quantum-dot array induced by an external electric field. In this system, the metal-insulator transition goes through a heavy electron phase in which the density of correlated electrons fluctuates.     

Rotating electrons in quantum dots: Classical limit

We solve the problem of a few electrons in a two-dimensional harmonic confinement using a quantum mechanical exact diagonalization technique, on the one hand, and classical mechanics, on the other. The quantitative agreement between the results of these two calculations suggests that, at low filling factors, all the low energy excitations of a quantum Hall liquid are classical vibrations of localized electrons. The Coriolis force plays a dominant role in determining the classical vibration frequencies.     

Magnetic dipole and electric quadrupole responses of elliptic quantum dots in magnetic fields

The magnetic dipole (M1) and electric quadupole (E2) responses of two-dimensional quantum dots with an elliptic shape are theoretically investigated as a function of the dot deformation and applied static magnetic field. Neglecting the electron-electron interaction we obtain analytical results which indicate the existence of four characteristic modes, with different B-dispersion of their energies and associated strengths. Interaction effects are numerically studied within the time-dependent local-spin-density and Hartree approximations, assessing the validity of the non-interacting picture. Received 29 November 2001 Published online 6 June 2002     

Zitterbewegung of electrons in quantum wells and dots in the presence of an in-plane magnetic field

We study the effect of an in-plane magnetic field on the zitterbewegung (ZB) of electrons in a semiconductor quantum well (QW) and in a quantum dot (QD) with the Rashba and Dresselhaus spin-orbit interactions (SOIs). We obtain a general expression of the time-evolution of the position vector and current of the electron in a semiconductor QW. The amplitude of the oscillatory motion is directly related to the Berry connection in momentum space. We find that in presence of the magnetic field the ZB in a QW does not vanish when the strengths of the Rashba and Dresselhaus SOIs are equal. The in-plane magnetic field helps to sustain the ZB in QWs even at a low value of k(0)d (where d is the width of the Gaussian wavepacket and k(0) is the initial wavevector). The trembling motion of an electron in a semiconductor QW with high Landé g-factor (e.g. InSb) is sustained over a long time, even at a low value of k(0)d. Further, we study the ZB of an electron in QDs within the two sub-band model numerically. The trembling motion persists in time even when the magnetic field is absent as well as when the strengths of the SOI are equal. The ZB in QDs is due to the superposition of oscillatory motions corresponding to all possible differences of the energy eigenvalues of the system. This is an another example of multi-frequency ZB phenomenon.     

Spin interactions in a quantum ring containing a magnetic impurity

The exciton states in a CdTe semiconductor quantum ring containing a single magnetic impurity are considered in an external magnetic field. The electron-hole spin interaction and s,p-d interactions between electron, hole and magnetic impurity are also taken into account in the calculations. It is shown that due to the s,p-d spin interactions the ground state exciton energy splits into 12 doubly degenerated energy levels. The external magnetic field removes this degeneracy. A novel method is proposed here to determine the values of the strengths of s,p-d interactions. The optical spectrum of the system for different polarizations of the incident light and for different initial states of the magnetic impurity spin projection is also studied.     

Auxiliary field quantum Monte-Carlo simulation of interacting electrons in quantum dots

Accurate auxiliary field quantum Monte-Carlo (AFQMC) simulations of interacting electrons in quantum dots are reported. Two different formulations of this approach are presented both of which have been designed specifically for application to quantum dots. A deflation technique for calculation of anti-symmetrized traces is introduced. The auxiliary field is sampled with a hybrid algorithm and the artificial dynamics needed for use with the present formulation of AFQMC is described. The constrained path approximation is used to control the sign problem. Results for the ground state energy of two spin-polarised, interacting electrons are presented and are found to agree well with exact diagonalization results for a wide range of screening lengths. The sign problem does not appear in the regime of small screening length.     

Analysis of inelastic scattering processes of electrons by localized electrons in quantum dots

The inelastic Coulomb scattering rate 1/τ_in of conduction electrons has been theoretically evaluated in the presence of localized states such as quantum dots. By a diagrammatical method, we have formulated 1/τ_in and its relation to the conductivity σ_loc(ω) through localized states. The dependence of τ_in on temperature T is examined in the case that σ_loc(ω) follows the Mott's model. It is found that 1/τ_in varies as T²(ln Δ/T)^d+1 where d is the dimensionality and Δ is tunneling energy between the localized states in the asymptonic T = 0 limit, in agreement with Imry's calculation. It is also found that calculated 1/τ_in deviates from T²(ln Δ/T)^d+1 as T increases, suggesting the importance of correction term at high temperature.     

Magnetic exchange energy of two-dimensional electrons

The exchange energy of a two-dimensional electron gas was evaluated exactly in the presence of a magnetic field when only the lowest Landau level is occupied fractionally.     

Magnetic properties of quantum dots and rings

Exact many-body methods as well as current-spin-density functional theory are used to study the magnetism and electron localization in two-dimensional quantum dots and quasi-one-dimensional quantum rings. Predictions of broken-symmetry solutions within the density functional model are confirmed by exact configuration interaction (CI) calculations: In a quantum ring the electrons localize to form an antiferromagnetic chain which can be described with a simple model Hamiltonian. In a quantum dot the magnetic field localizes the electrons as predicted with the density functional approach. Received 5 December 2000     

Magnetic interaction between coupled quantum dots

We study the magnetic coupling in artificial molecules composed of two and four laterally coupled quantum dots. The electronic ground-state configurations of such systems are determined by applying current spin density functional theory which allows to include effects of magnetic fields. While the ground-state of a two-dot molecule with strong enough inter-dot coupling tends to be antiferromagnetic with respect to the spins of the single dot components, we find that a square lattice of four dots has a ferromagnetic ground state. Received 17 February 1999 and Received in final form 1 June 1999     

One-spin quantum logic gates from exchange interactions and a global magnetic field

It has been widely assumed that one-qubit gates in spin-based quantum computers suffer from severe technical difficulties. We show that one-qubit gates can, in fact, be generated using only modest and presently feasible technological requirements. Our solution uses only global magnetic fields and controllable Heisenberg exchange interactions, thus circumventing the need for single-spin addressing.     

Dynamic localization of two electrons in AC-driven triple quantum dots and quantum dot shuttles

We analyze the dynamic localization of two interacting electrons induced by alternating current electric fields in triple quantum dots and triple quantum dot shuttles. The calculation of the long-time averaged occupation probability shows that both the intra-and inter-dot Coulomb interaction can increase the localization of electrons even when the AC field is not very large. The mechanical oscillation of the quantum dot shuttles may keep the localization of electrons at a high level within a range if its frequency is quite a bit smaller than the AC field. However, the localization may be depressed if the frequency of the mechanical oscillation is the integer times of the frequency of the AC field. We also derive the analytical condition of two-electron localization both for triple quantum dots and quantum dot shuttles within the Floquet formalism.