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arXiv:0811.2945 · Physical Review B

Magnetic field dependence of the many-electron states in a magnetic quantum dot: The ferromagnetic-antiferromagnetic transition

Nga T. T. Nguyen, François Maria Peeters

Published Jul 25, 2008• 49 citations
arXivHTMLPDF

Abstract

The electron-electron correlations in a many-electron $({N}_{e}=1,2,\dots{},5)$ quantum dot confined by a parabolic potential is investigated in the presence of a single magnetic ion and a perpendicular magnetic field. We obtained the energy spectrum and calculated the addition energy which exhibits cusps as a function of the magnetic field. The vortex properties of the many-particle wave function of the ground state are studied and for large magnetic fields are related to composite fermions. The position of the impurity influences strongly the spin-pair-correlation function when the external field is large. In a small applied magnetic field, the spin-exchange energy together with the Zeeman terms leads to a ferromagnetic-antiferromagnetic (FM-AFM) transition. When the magnetic ion is shifted away from the center of the quantum dot, a remarkable re-entrant AFM-FM-AFM transition is found as a function of the strength of the Coulomb interaction. Thermodynamic quantities such as the heat capacity, the magnetization, and the susceptibility are also studied. The cusps in the energy levels show up as peaks in the heat capacity and the susceptibility.

DOI
10.1103/physrevb.78.045321

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By nonperturbatively solving the nonequilibrium Anderson two-impurity model with the hierarchical equations of motion approach, we report a robust ferromagnetic (FM) phase in series-coupled double quantum dots, which can suppress the antiferromagnetic (AFM) phase and dominate the phase diagram at finite bias and detuning energy in the strongly correlated limit. The FM exchange interaction origins from the passive parallel spin arrangement caused by the Pauli exclusion principle during the electrons transport. At very low temperature, the Kondo screening of the magnetic moment in the FM phase induces some nonequilibrium Kondo effects in magnetic susceptibility, spectral functions and current. In the weakly correlated limit, the AFM phase is found still stable, therefore, a magnetic-field-free internal control of spin states can be expected through the continuous FM-AFM phase transition.
We study the low-temperature transport properties of systems of parallel quantum dots described by the NNN-impurity Anderson model. We calculate the quasiparticle scattering phase shifts, spectral functions, and correlations as a function of the gate voltage for NNN up to 5. For any NNN, the conductance at the particle-hole symmetric point is unitary. For $N\ensuremath{\ge}2$, a transition from ferromagnetic to antiferromagnetic impurity spin correlations occurs at some gate voltage. For $N\ensuremath{\ge}3$, there is an additional transition due to an abrupt change in average impurity occupancy. For odd NNN, the conductance is discontinuous through both quantum phase transitions, while for even NNN only the magnetic transition affects the conductance. Similar effects should be experimentally observable in systems of quantum dots with ferromagnetic conduction-band-mediated interdot exchange interactions.
Correlation and magnetic effects in narrow bands are studied using a new type of self-consistent cluster treatment of Hubbard's Hamiltonian. Here the dynamics consist of electron hopping between lattice sites and Coulomb repulsion between electrons only on the same site. The environment of the cluster is regarded as a particle reservoir, one such for each spin. Hopping between the cluster and reservoirs is described by fermion source terms. It is required that the thermodynamic average of the particle currents of each spin within the cluster equal the corresponding particle exchange between cluster and reservoir. Electron motion in the system is examined for varying ratios of the strength of the hopping to the Coulomb repulsion. This is done as a function of electron density, spin, temperature, and external magnetic field. A Mott transition is found under dynamical conditions close to those predicted by Hubbard when there is one particle per site. For 〈n〉 ≠ 1, no metal insulator transition exists although discontinuous changes in the cluster-reservoir coupling occur. The magnetic susceptibility of the cluster reveals antiferromagnetic behavior for 〈n〉 = 1, ferromagnetic behavior for 〈n〉 > 1, and partial ferromagnetic character for n < 1. This appears to agree with Nagoaka's results.
Quantum entanglement is analyzed thoroughly in the case of the ground and lowest states of two-electron axially symmetric quantum dots under a perpendicular magnetic field. The individual-particle and the center-of-mass representations are used to study the entanglement variation at the transition from interacting to noninteracting particle regimes. The mechanism of symmetry breaking due to the interaction, which results in the states with symmetries related to the latter representation only being entangled even at the vanishing interaction, is discussed. The analytical expression for the entanglement measure based on the linear entropy is derived in the limit of noninteracting electrons. It reproduces remarkably well the numerical results for the lowest states with the magnetic quantum number $M\ensuremath{\ge}2$ in the interacting regime. It is found that the entanglement of the ground state is a discontinuous function of the field strength. A method to estimate the entanglement of the ground state, characterized by the quantum number MMM, with the aid of the magnetic-field dependence of the addition energy is proposed.
The ground states of parabolically confined electrons in a quantum dot are studied by both direct numerical diagonalization and quantum Monte Carlo (QMC) methods. We present a simple but accurate variational many-body wave function for the dot in the limit of a weak magnetic field. The wave function has the center-of-mass motion restricted to the lowest-energy state and the electron-electron interaction is taken into account by a Jastrow two-body correlation factor. The optimized wave function has an accuracy very close to the state-of-the-art numerical diagonalization calculations. The results and the computational efficiency indicate that the presented wave function combined with the QMC method suits ideally for studies of large quantum dots.
Based on the variational method of Pekar type, we study the energies and the wave-functions of the ground and the first-excited states of magneto-bipolaron, which is strongly coupled to the LO phonon in a parabolic potential quantum dot under an applied magnetic field, thus built up a quantum dot magneto-bipolaron qubit. The results show that the oscillation period of the probability density of the two electrons in the qubit decreases with increasing electron–phonon coupling strength α , resonant frequency of the magnetic field ω c , confinement strength of the quantum dot ω 0 , and dielectric constant ratio of the medium η ; the probability density of the two electrons in the qubit oscillates periodically with increasing time t , angular coordinate φ 2 , and dielectric constant ratio of the medium η ; the probability of electron appearing near the center of the quantum dot is larger, and the probability of electron appearing away from the center of the quantum dot is much smaller.