## Efeitos de interações elétron-elétron e spin-órbita nas propriedades magneto-eletrônicas de magneto-transporte de sistemas confinados.

##### Abstract

Effects of the direct and exchange electron-electron interaction, external magnetic
field, symmetry of the charge carriers confining potential, radius, material g-factor, and
also of the spin-orbit interaction in zincblende structure materials, are treated on the
electronic and transport properties of semiconductor quantum dots (islands) charged by
many particles. Three distinct kinds of confining potentials are considered: spherical,
parabolic, and quasi-one-dimensional which, respectively, define a three-dimensional,
two-dimensional, and one-dimensional island; the first one is more appropriated for the
description of quantum dots formed in glassy matrices, while the last two better describe
quantum dots litographically defined in a two-dimensional electron gas.
Transport properties are considered in the spherical and quasi-one-dimensional
islands, where we assume that the electronic current is in the resonant tunneling ballistic
and coherent regimes, with essential role played by the excited states of the specific
symmetry. We show that different geometries induce distinct level ordering in the island
and that there is, in addition to the usual spin blockade, another kind of blockade
mechanism which influences the system current; we label it by orbital blockade, because
it is essentially due to the structure geometric confinement.
We calculate the electronic spectrum of the many-particle system according to its
symmetry. In the spherical case, we firstly use the LS-coupling scheme in order to obtain
the eigenstates of an island charged by 3 electrons, following the orbital L and spin S total
angular momentum addiction rules; we consider intensities of the magnetic field that
allow us to neglect its diamagnetic contribution; the electron-electron interaction is
treated as a perturbation in a Hartree-Fock way. In the following we use, in this same
symmetry, the Roothaan and Pople-Nesbet matrix methods in order to deal with islands
charged by 40 electrons, where the addition spectrum is calculated and Hund s rule is
verified; we show how a magnetic field is able to violate such rule. The advantage of this
numerical approach is the possibility to deal with a very high occupation in the island; the
disadvantage is that their eigenstates do not have defined L and S values, as it is the case
in the LS-coupling scheme.
In the parabolic case, we employ a numerical diagonalization in order to obtain
the island eigenstates charged by 2 electrons, without any restrictions regarding the
magnetic field intensity or the system radius; we take into account both possible spinorbit
couplings, one related to the implicit absence of zincblende crystalline structure
inversion symmetry (Dresselhaus effect), and the other one related to the absence of
structure inversion symmetry as caused by the confinement defining the two-dimensional
electron gas (Rashba effect); we analyze the critical magnetic fields where both effects
give origin to a intrinsic spin mixture in the island, inducing level anticrossings in the
Fock-Darwin spectrum where intense spin-flips processes occur. In the quasi-onedimensional
case, we just reproduce a known spectrum for an island charged by 4
electrons.