Theoretical Studies of Spin-Dependent Quantum Phenomena in Semiconductor Nanostructures

Sammanfattning: The study of spin transport has emerged at the forefront of condensed matter physics during the last decade. Much of the interest has undoubtedly been sparked by the advent of the spintronics paradigm and the idea of creating novel electronic devices based on the spin degree of freedom of the carriers. However, a great deal of interest is due to the rich physics that emerges from the study of spin phenomena. In this thesis we will study quantum spin-dependent phenomena as it appears in nano-scale structures formed in semiconducting materials. We will set up a formalism for quantum spin transport and apply it to investigate novel coherent spin phenomena such as the spin Hall effect and Zitterbewegung, as well as spin conductance and polarisation in mesoscopic structures. Symmetry relations are derived which sets rigorous constraints on the spin transport properties. We will furthermore consider many-body effects in spin-orbit coupled systems and coherent geometrical phase properties due to interaction with a time-periodic field. Computational techniques based on the scattering matrix formalism have been developed for spin-dependent transport in quantum structures with spin-orbit interaction and local magnetic field modulations. The techniques have been applied to the studies of the spin Hall effect and Zitterbewegung in both electron and the less studied hole systems, multi-terminal spin-dependent transport with spin-orbit interaction, and the problem of creating a source of spin-polarised carriers. In the presence of spin-orbit interactions the spin Hall effect arises as a spin accumulation along the transverse edges of a waveguide, and as a spin-stripe pattern in the internal part of the waveguide. We show that the Zitterbewegung is directly linked to the spin Hall effect and only differ in the injection conditions. We further find that flux polarisation in a multi-terminal structure is strongly influenced by the existence of multiple lead channels and give rise to spin-rectification and spin-partitioning. A source of spin-polarised carriers is proposed by demonstrating that a current of large spin polarisation, at a temperature above the spin-splitting temperature, can be achieved in a double-dot structure influenced by a non-uniform magnetic field. Symmetry considerations are powerful tools to derive rigorous constraints on spin transport properties. By a symmetry analysis we show that the in-plane polarisation of hole transport necessarily vanishes whenever the outgoing lead only supports heavy hole channels. It is also shown that the complete spin-polarisation vanishes identically under time-reversal symmetry whenever the outgoing lead supports one, doubly degenerate, hole channel independent of the number of incoming channels or the details of the scatterer. On the topic of interactions, recent measurements of Coulomb blockade of holes in nanowire quantum dots are analysed by formulating a pseudo-spin Hartree-Fock language to extract a hole exchange interaction energy. We furthermore study the geometrical response of quantum confined particles to a time-periodic electric field and show that field-induced angular momentum and spin transitions are associated with a geometrical phase indicating a non-trivial topology of the projective Hilbert space.

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