Maier, Franziska. Holes in nanowires and quantum dots : spin qubits, majorana fermions, and hole and hyperfine interactions. 2015, PhD Thesis, University of Basel, Faculty of Science.

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Official URL: http://edoc.unibas.ch/diss/DissB_11152
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Abstract
In the last decades much scientific effort was spent on manufacturing and understanding the properties of smaller and smaller condensed matter systems. This eventually resulted in the reliable production of semiconductor quantum dots and nanowires, systems that are reduced to sizes of several (tens of) nanometers in all three or at least two dimensions. The confinement in such nanoscale systems is so strong that quantum effects play a crucial role. Furthermore, the exact energy level or band structure of these systems depends heavily on the material composition, the precise confinement geometry, the intrinsic strain distribution, the spinorbit interaction, as well as the presence of intrinsic and externally applied electric and magnetic fields.
The feasibility of loading only a single charge carrier onto a quantum dot led to the proposal of the spin qubit, as a possible smallest building block of a semiconductorbased quantum computer. In a spin qubit the quantum information is stored in a superposition of Zeemansplit spinup and spindown states. Most crucial for its successful implementation is the reliable control and the proper understanding of the carrier spin dynamics. Solving this task has been a highly active research field ever since, both on the experimental and theoretical side. Most of the research conducted so far focused on electrons in the lowest conduction band states. However, at some point it was realized that holes in the states close to the valence band edge may sometimes offer a more advantageous behavior regarding qubit control and coherence. This is due to the ptype symmetry of the associated Bloch states which results in a strong spinorbit interaction on the atomic level and in an anisotropic hyperfine interaction that is much weaker than the hyperfine interaction of electrons.
Semiconductor nanowires can serve both as hosts for quantum dots and as onedimensional channels. Nanowire quantum dots are defined by putting additional closely spaced gates on the nanowire that allow for an electrically tunable longitudinal confinement. Otherwise, a onedimensional electron or hole gas forms inside the nanowire. Additionally, it has been proposed that nanowires with strong spinorbit interaction can be employed as hosts for Majorana fermions. This is of special interest because their nonabelian braiding statistics make Majorana fermions good candidates for topological qubits.
In the first part of this thesis, we focus mostly on holes and hole spins confined to selfassembled quantum dots and quantum dots defined in Ge/Si core/shell nanowires. We calculate the hole spin relaxation and decoherence times in these quantum dots due to holespin phonon interactions and holespin nuclearspin interactions that are mediated by the spinorbit interaction and the hyperfine interaction, respectively. Subsequently, we show how these times are affected by specific system parameters such as intrinsic and extrinsic strain, the confinement strength as well as the magnitude and direction of applied electric and magnetic fields. Furthermore, we determine the effective Zeeman splitting by investigating the anisotropy and tunability of the effective g factor of electrons and holes in the lowest energy levels in these systems. In addition, we investigate the effect of noncollinear terms in the holespin nuclearspin hyperfine interaction which reduce the degree of nuclear spin polarization that can be obtained by optical pumping. Also, we propose an experimental setup that allows to detect and quantify this effect.
In the second part of this work we survey holes in Ge/Si core/shell nanowires by employing an effective onedimensional microscopic model that includes a strong and electrically tunable Rashbatype spinorbit interaction. Using a Luttinger liquid description, we show that a screened Coulomb interaction strongly influences the nanowire properties. The strength of the interactions is explicitly quantified by calculating the scaling exponents of correlation functions and by examining the effect of the interactions on a partial gap opened by a small magnetic field.
Finally, we consider the nanowires as hosts for Majorana fermions. This is possible when the nanowire is placed in close proximity to an swave superconductor and put into a helical regime by applying electric fields. Furthermore, a magnetic field is needed to open a gap in the spectrum. In this setup, we calculate the field dependence of the localization lengths of the associated Majorana fermion wave functions. In short nanowires the Majorana fermions hybridize and form a subgap fermion whose energy oscillates as a function of the applied fields. The oscillation period allows to measure the strength of the spinorbit interaction and the g factor anisotropy of the nanowire.
The feasibility of loading only a single charge carrier onto a quantum dot led to the proposal of the spin qubit, as a possible smallest building block of a semiconductorbased quantum computer. In a spin qubit the quantum information is stored in a superposition of Zeemansplit spinup and spindown states. Most crucial for its successful implementation is the reliable control and the proper understanding of the carrier spin dynamics. Solving this task has been a highly active research field ever since, both on the experimental and theoretical side. Most of the research conducted so far focused on electrons in the lowest conduction band states. However, at some point it was realized that holes in the states close to the valence band edge may sometimes offer a more advantageous behavior regarding qubit control and coherence. This is due to the ptype symmetry of the associated Bloch states which results in a strong spinorbit interaction on the atomic level and in an anisotropic hyperfine interaction that is much weaker than the hyperfine interaction of electrons.
Semiconductor nanowires can serve both as hosts for quantum dots and as onedimensional channels. Nanowire quantum dots are defined by putting additional closely spaced gates on the nanowire that allow for an electrically tunable longitudinal confinement. Otherwise, a onedimensional electron or hole gas forms inside the nanowire. Additionally, it has been proposed that nanowires with strong spinorbit interaction can be employed as hosts for Majorana fermions. This is of special interest because their nonabelian braiding statistics make Majorana fermions good candidates for topological qubits.
In the first part of this thesis, we focus mostly on holes and hole spins confined to selfassembled quantum dots and quantum dots defined in Ge/Si core/shell nanowires. We calculate the hole spin relaxation and decoherence times in these quantum dots due to holespin phonon interactions and holespin nuclearspin interactions that are mediated by the spinorbit interaction and the hyperfine interaction, respectively. Subsequently, we show how these times are affected by specific system parameters such as intrinsic and extrinsic strain, the confinement strength as well as the magnitude and direction of applied electric and magnetic fields. Furthermore, we determine the effective Zeeman splitting by investigating the anisotropy and tunability of the effective g factor of electrons and holes in the lowest energy levels in these systems. In addition, we investigate the effect of noncollinear terms in the holespin nuclearspin hyperfine interaction which reduce the degree of nuclear spin polarization that can be obtained by optical pumping. Also, we propose an experimental setup that allows to detect and quantify this effect.
In the second part of this work we survey holes in Ge/Si core/shell nanowires by employing an effective onedimensional microscopic model that includes a strong and electrically tunable Rashbatype spinorbit interaction. Using a Luttinger liquid description, we show that a screened Coulomb interaction strongly influences the nanowire properties. The strength of the interactions is explicitly quantified by calculating the scaling exponents of correlation functions and by examining the effect of the interactions on a partial gap opened by a small magnetic field.
Finally, we consider the nanowires as hosts for Majorana fermions. This is possible when the nanowire is placed in close proximity to an swave superconductor and put into a helical regime by applying electric fields. Furthermore, a magnetic field is needed to open a gap in the spectrum. In this setup, we calculate the field dependence of the localization lengths of the associated Majorana fermion wave functions. In short nanowires the Majorana fermions hybridize and form a subgap fermion whose energy oscillates as a function of the applied fields. The oscillation period allows to measure the strength of the spinorbit interaction and the g factor anisotropy of the nanowire.
Advisors:  Loss, Daniel 

Committee Members:  Stano, Peter 
Faculties and Departments:  05 Faculty of Science > Departement Physik > Physik > Theoretische Physik Mesoscopics (Loss) 
UniBasel Contributors:  Maier, Franziska and Loss, Daniel 
Item Type:  Thesis 
Thesis Subtype:  Doctoral Thesis 
Thesis no:  11152 
Thesis status:  Complete 
Bibsysno:  Link to catalogue 
Number of Pages:  155 p. 
Language:  English 
Identification Number: 

Last Modified:  22 Jan 2018 15:52 
Deposited On:  27 Mar 2015 09:03 
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