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%0 Thesis
%A Sharma, Mira Ramakant
%T Spin-orbit coupling, entanglement, and topological structures of the g-tensor of crystalline materials for spin qubits
%I RWTH Aachen University
%V Dissertation
%C Aachen
%M RWTH-2025-06868
%P 1 Online-Ressource : Illustrationen
%D 2025
%Z Veröffentlicht auf dem Publikationsserver der RWTH Aachen University
%Z Dissertation, RWTH Aachen University, 2025
%X Semiconductor spin qubits hosted in quantum dots are emerging as promising candidates for scalable quantum computing due to their ease of integration into current semiconductor technology and long coherence times. Spin-orbit effects play a significant role in the manipulation of such qubits and could at the same time contribute to noise. The role of the g-factor, which is characteristic of the spin-orbit interaction (SOI), is paramount to the realization of scalable and robust information processing using spin qubits. It is an intrinsic one-electron property that characterizes the magnetic moment of Kramers-degenerate states. Even in a device structure like a quantum dot, the g-factor is largely governed by the underlying crystal physics, as explored in this work.The g-tensor is of increasing importance in the current design of spin qubits. It is affected by details of heterostructure composition, disorder, and electric fields, but, as shown in this work, inherits much of its structure from the effect of the spin-orbit interaction working at the crystal-lattice level. We observe that the g-tensor is composed of a spin contribution gS and an orbital contribution gL, g = gL + gS. We show that the orbital g-tensor can be obtained from the Luttinger theory as well as from an equivalent formalism of the band Berry curvature. Using tight-binding, we give formal expressions for the two contributions for important valence and conduction bands in silicon, germanium, and gallium arsenide. For all crystals with high (cubic) symmetry, we show that large departures from the nonrelativistic value g = 2 are guaranteed by symmetry. In particular, considering the spin part gS(k), we prove that the scalar function det(gS(k)) must go to zero on closed surfaces in the Brillouin zone, no matter how weak the spin-orbit coupling is. We also prove that for wave vectors k on these surfaces, the Bloch states  - u_nk> have maximal spin-orbital entanglement. Using tight-binding calculations, we observe that the surfaces det(g(k)) = 0 exhibit many interesting topological features, exhibiting Lifshitz critical points as understood in Fermi-surface theory. We further explore the origins of the orbital contribution, gL, by defining a current density operator, J(Ri,Rj) along bonds Rj-Ri between atoms. These topological features of the -tensor can be exploited to theoretically obtain the g-factors for electron spins in heterostructures where it may be difficult to experimentally probe them.
%F PUB:(DE-HGF)11
%9 Dissertation / PhD Thesis
%R 10.18154/RWTH-2025-06868
%U https://publications.rwth-aachen.de/record/1016292