Hole spin relaxation time due to the hole--acoustic-phonon scattering in $\mathrm{GaAs}$ quantum dots confined in quantum wells along (001) and (111) directions is studied after the exact diagonalization of Luttinger Hamiltonian. Different effects such as strain, magnetic field, quantum dot diameter, quantum well width, and the temperature on the spin relaxation time are investigated thoroughly. Many features that are quite different from the electron spin relaxation in quantum dots and quantum wells are presented with the underlying physics elaborated.

http://arxiv.org/pdf/cond-mat/0409249.pdf

Hole spin relaxation in semiconductor quantum dots

Magnetic semiconductor quantum dots with a few carriers represent an interesting model system where ferromagnetic interactions can be tuned by voltage. By designing the geometry of a doped quantum dot, one can tailor the anisotropic quantum states of magnetic polarons. The strong anisotropy of magnetic polaron states in disklike quantum dots with holes comes from the spin splitting in the valence band. The binding energy and spontaneous magnetization of quantum dots oscillate with the number of particles and reflect the shell structure. Due to the Coulomb interaction, the maximum binding energy and spin polarization of magnetic polarons occur in the regime of Hund’s rule when the total spin of holes in a quantum dot is maximum. With increasing number of particles in a quantum dot and for certain orbital configurations, the ferromagnetic state becomes especially stable or may have broken symmetry. In quantum dots with a strong ferromagnetic interaction, the ground state can undergo a transition from a magnetic to a nonmagnetic state with increasing temperature or decreasing exchange interaction. The characteristic temperature and fluctuations of magnetic polarons depend on the binding energy and degeneracy of the shell. The capacitance spectra of magnetic quantum dots with few particles reveal the formation of polaron states.

http://plato.phy.ohiou.edu/~govorov/PRBMnquantumdotfewelect.pdf

Voltage-tunable ferromagnetism in semimagnetic quantum dots with few particles: Magnetic polarons and electrical capacitance

We describe a model device allowing voltage control of the magnetic properties of magnetic ions in III-V self-assembled semiconductor quantum dots. The applied voltage, combined with Coulomb blockade, allows the control of the number of holes in the quantum dot. The spins of the holes interact with the spins of the magnetic ions via $\mathit{sp}\text{\ensuremath{-}}d$ exchange interactions. The spectrum of a Mn ion in a $p$-type InAs quantum disk in a magnetic field is calculated as a function of the number of holes described by the Luttinger-Kohn Hamiltonian. For a neutral Mn acceptor, the spin of the hole leads to an effective magnetic field which strongly modifies the magnetization of the ion. The magnetization can be modified further by charging the dot with an additional hole. The interacting holes form a singlet parity ground state, suppress the effective field and modify the magnetic moment of the charged complex.

Voltage control of the magnetic properties of charged semiconductor quantum dots containing magnetic ions

Many-particle electron states in semiconductor quantum dots with carrier-mediated ferromagnetism are studied theoretically within the self-consistent Boltzmann equation formalism. Depending on the conditions, a quantum dot may contain there phases: partially spin-polarized ferromagnetic, fully spin-polarized ferromagnetic, and paramagnetic phases. The physical properties of many-body ferromagnetic confined systems come from the competing carrier-mediated ferromagnetic and Coulomb interactions. The magnetic phases in gated quantum dots with holes can be controlled by the voltage or via optical methods.

Thomas-Fermi model and ferromagnetic phases of magnetic semiconductor quantum dots

Anisotropic magnetic-field evolution of the valence-band states in ideal ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$ quantum wire structures have been studied theoretically by using multiband effective-mass method. The heavy- and light-hole bands show significant mixing owing to both the one-dimensional quantum confinement and the p-d exchange interaction. Because of the anisotropy of the initial quantization condition determined by the one-dimensional confinement, the Zeeman diagram of the valence bands exhibits anisotropic characteristics depending on the direction of the external magnetic field. According to the magnetic-field evolution of the valence-band states, the optical transition probability shows a dramatic change in the polarization.

/pdf/anisotropic-magneto-optical-effects-in-one-dimensional-3mh75yv8qe.pdf

Anisotropic magneto-optical effects in one-dimensional diluted magnetic semiconductors

The electronic structure of a diluted magnetic semiconductor (DMS) quantum dot (QD) is studied within the framework of the effective-mass theory. We find that the energies of the electron with different spin orientation exhibit different behavior as a function of magnetic field at small magnetic fields. The energies of the hole decreases rapidly at low magnetic fields and saturate at higher magnetic field due to the sp-d exchange interaction between the carriers and the magnetic ions. The mixing effect of the hole states in the DMS QD can be tuned by changing the external magnetic field. An interesting crossing behavior of the hole ground state between the heavy-hole state and the light-hole state is found with variation of the QD radius. The strength of the interband optical transition for different circular polarization exhibts quite different behavior with increasing magnetic field and QD radius.

/pdf/electron-and-hole-states-in-diluted-magnetic-semiconductor-3s6z6nntlf.pdf

F. M. Peeters

Papers

Electron and hole states in diluted magnetic semiconductor quantum dots