Quasiparticle transport and g factor anisotropy in quantum dots

Current computer systems encode data in sequences of the binary unit, the bit. The quest of designing faster processors is one of the most important in modern society. However, reducing the size of transistors and thus CPUs is limited to the size of single atoms. Modern fabrication techniques employed in industry achieve structures at scales down to 22nm. Hence, new computation schemes are necessary to continue construction of better processors. Expanding the properties of the bit is a scheme widely spread in the condensed matter community. The most promising ansatz is to enable the bit to not only take states 0 and 1 but also any superposition of the two and thus providing a new set of operations. Essentially, this concept takes the bit into the world of quantum mechanics and marks the genesis of the qubit. Numerous proposal for the implementation of the qubit exist. However, an electron spin confined to a quantum dot (QD) turns out to be the most natural realization of the qubit. Hence, knowledge of QD properties is essential to the fabrication of an efficient and powerful quantum computer.
In the first part of this thesis we study a QD tunnel coupled to one dimensional conductors (1D), in particular edge states of fractional quantum Hall (FQH) samples. Our proposed setup combines two regimes that individually attract tremendous scientific effort. The QD is in the Coulomb blockade regime. Hence sequential tunneling processes from edge state via the QD to the other edge state are suppressed. Thus, we focus on cotunneling, i.e.\ second order processes transferring a particle directly from one edge to the other. 1D conductors are strongly correlated systems that reveal interesting elementary excitations. Especially FQH edge states at filling factor 5/2 have been identified to exhibit excitations obeying non-Abelian statistics. Renormalization group calculations show that the relevant excitations are quasiparticles of both quarter and half of the elementary charge. We determine the cotunneling conductance via the QD for different kinds of charge carriers, in particular electrons and quasiparticles of fractional charge e/2 and e/4. On the one hand, we find that the electron cotunneling conductance is strongly suppressed while on the other hand both e/2 and e/4 quasiparticles exhibit distinctive signatures in the cotunneling lineshapes. Our findings provide a test of the Moore-Read wavefunction based on a simple transport measurement.
The second part is devoted to the response of a qubit to external fields. In particular, we study the electron spins confined to self-assembled InAs QDs of pyramidal shape. We present a trial wavefunction obeying hard-wall boundary conditions for a pyramidal geometry. Starting from the band structure of the bulk material we model the QD by adding strain and hard-wall confinement potential according to the considered geometry. Furthermore, we account for external electric and magnetic fields. We decouple the conduction band from the valence band and find the spectrum of the bound electron states in the QD. Finally, we extract the g factor and analyze the dependence on the direction of the external fields. Depending on the respective electronic states, we find a variety of g factor anisotropies suitable for determination by a simple transport measurement. We find both qualitatively good agreement with recent measurements and shapes not yet observed in experiments. At last, we conclude that our findings can be employed to control the splitting of qubit states and therefore should prove useful for qubit manipulation.