Intoductory material
Molecular Electronics Group

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 spin-split 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 locally-screened 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 (Vg) on the spin-splitting 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 Vg-dependence of the QD level spin-splitting strongly depends on the shape of the density of states (DOS). For one class of DOS shapes there is nearly no Vg-dependence, for another, Vg can be used to control the magnitude and sign of the spin-splitting, which can be interpreted as a local exchange magnetic field. We find that the spin-splitting acquires a new type of logarithmic divergence. We give an analytical explanation for our numerical results and explain how they arise due to spin-dependent charge fluctuations.

Recent experiments measuring the emission of exciton recombination in a self-organized 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 many-body 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 zero-temperature 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 well-known X-ray edge absorption problem. Secondly, the threshold energy ω0 - 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 Uexc.

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 turn-stiles 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 inter-dot 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 low-energy 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 magneto-conductance 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.