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Hyperfine and Spin-Orbit Interactions in Semiconductor Nanostructures
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Dissertation
Hyperfine and Spin-Orbit Interactions in Semiconductor Nanostructures
2020
Overview
Understanding the hyperfine and spin-orbit interactions is important for e.g. quantum information processing with spin qubits. In this thesis, we investigate these interactions in various semiconductor nanostructures. While the methods developed here have been applied to specific nanostructures, they can be generalized to understand interactions (hyperfine, spin-orbit, and potentially others) in other systems and/or materials.This thesis includes an introductory chapter where we derive the hyperfine and spin-orbit interactions from the Dirac equation and discuss the main theoretical tools used throughout the text, k · p theory and density-functional theory. In the succeeding chapter, we calculate the hyperfine couplings for electrons and holes in GaAs and silicon through first-principles density-functional theory. Our results are consistent with Knight-shift measurements for electrons. For holes, experimental results are still limited and a direct comparison to experiment is not possible. In the third chapter, we relate the dynamics of a hole spin after a spin echo pulse sequence to the hole hyperfine coupling. In particular, we demonstrate how the hole hyperfine couplings can be determined from measurements of hole spin echo envelope modulations. We apply this concept to a boron acceptor in silicon, where the value of the hyperfine coupling remains an open question. We show that direct measurements of boron-acceptor hyperfine couplings can be obtained by modifying the direction of the applied magnetic field in existing experiments. Finally, in the fourth chapter, we extend k · p theory beyond the envelope function approximation. In doing so, we find a novel 'dipolar' heavy-hole spin-orbit coupling in III-V semiconductor asymmetric quantum wells. This spin-orbit coupling is parametrized by the heavy-hole/light-hole electric-dipole matrix element. We calculate this matrix element and show that in GaAs, the dipolar spin-orbit coupling can represent a significant portion of the linear Dresselhaus spin-orbit coupling.
Publisher
ProQuest Dissertations & Theses
Subject
ISBN
9798708708694
