

The Kondo effect in quantum dots (QDs)  artificial magnetic impurities  attached to ferromagnetic leads is studied with the numerical renormalization group (NRG) method. It is shown that the QD level is spinsplit due to presence of ferromagnetic electrodes, leading to a suppression of the Kondo effect. We find that the Kondo effect can be restored by compensating this splitting with a magnetic field. Although the resulting Kondo resonance then has an unusual spin asymmetry with a reduced Kondo temperature, the ground state is still a locallyscreened state, describable by Fermi liquid theory and a generalized Friedel sum rule, and transport in the unitary limit is not spin dependent.
The effect of a gate voltage (V_{g}) on the spinsplitting of an electronic level in a quantum dot attached to ferromagnetic leads is studied in the Kondo regime using a generalized numerical renormalization group technique. We find that the V_{g}dependence of the QD level spinsplitting strongly depends on the shape of the density of states (DOS). For one class of DOS shapes there is nearly no V_{g}dependence, for another, V_{g} can be used to control the magnitude and sign of the spinsplitting, which can be interpreted as a local exchange magnetic field. We find that the spinsplitting acquires a new type of logarithmic divergence. We give an analytical explanation for our numerical results and explain how they arise due to spindependent charge fluctuations.

Recent experiments measuring the emission of exciton recombination in a selforganized single quantum dot (QD) have revealed that novel effects occur when the wetting layer surrounding the QD becomes filled with electrons, because the resulting Fermi sea can hybridize with the local electron levels on the dot. Motivated by these experiments, we study an extended Anderson model, which describes a local conduction band level coupled to a Fermi sea, but also includes a local valence band level. We are interested, in particular, on how manybody correlations resulting from the presence of the Fermi sea affect the absorption and emission spectra. Using Wilson's numerical renormalization group method, we calculate the zerotemperature absorption (emission) spectrum of a QD which starts from (ends up in) a strongly correlated Kondo ground state. We predict two features: Firstly, we find that the spectrum shows a power law divergence close to the threshold, with an exponent that can be understood by analogy to the wellknown Xray edge absorption problem. Secondly, the threshold energy ω_{0}  below which no photon is absorbed (above which no photon is emitted)  shows a marked, monotonic shift as a function of the exciton binding energy U_{exc}.

The simplest mesoscopic circuits that go beyond
single dot devices in their complexity are double dot devices
. These 'artificial molecules'
have been extensively studied both
theoretically
and experimentally:
They may give rise to stochastic Coulomb blockade and
peak splitting,
can be used as single electron pumps,
were proposed to measure high frequency quantum noise,
and are building blocks for more complicated
mesoscopic devices such as turnstiles or cellular automata.
Double dots also have interesting
degeneracy points where quantum fluctuations may
lead to unusual strongly correlated states.
We study a symmetrical double quantum dot system with strong capacitive interdot coupling using renormalization group methods. The dots are attached to separate leads, and there can be a weak tunneling between them. In the regime where there is a single electron on the DD the lowenergy behavior is characterized by an SU(4)symmetric Fermi liquid theory with entangled spin and charge Kondo correlations and a phase shift π/4. Application of an external magnetic field gives rise to a large magnetoconductance and a crossover to a purely charge Kondo state in the charge sector with SU(2) symmetry. In a four lead setup we find perfectly spin polarized transmission.


