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Main Authors: Sharma, Mira, DiVincenzo, David P.
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2402.06310
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author Sharma, Mira
DiVincenzo, David P.
author_facet Sharma, Mira
DiVincenzo, David P.
contents The $\bf{g}$ tensor, which determines the reaction of Kramers-degenerate states to an applied magnetic field, is of increasing importance in the current design of spin qubits. It is affected by details of heterostructure composition, disorder, and electric fields, but it inherits much of its structure from the effect of the spin-orbit interaction working at the crystal-lattice level. Here we uncover new symmetry and topological features of $\bf{g}=\bf{g}_L+\bf{g}_S$ 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 $\bf{g}_S(\bf{k})$, we prove that the scalar function $det(\bf{g}_S(\bf{k}))$ 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 $\bf{k}$ on these surfaces, the Bloch states $|u_{n\bf{k}}\rangle$ have maximal spin-orbital entanglement. Using tight-binding calculations, we observe that the surfaces $det(\bf{g}(\bf{k}))=0$ exhibit many interesting topological features, exhibiting Lifshitz critical points as understood in Fermi-surface theory.
format Preprint
id arxiv_https___arxiv_org_abs_2402_06310
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle g-factor symmetry and topology in semiconductor band states
Sharma, Mira
DiVincenzo, David P.
Quantum Physics
The $\bf{g}$ tensor, which determines the reaction of Kramers-degenerate states to an applied magnetic field, is of increasing importance in the current design of spin qubits. It is affected by details of heterostructure composition, disorder, and electric fields, but it inherits much of its structure from the effect of the spin-orbit interaction working at the crystal-lattice level. Here we uncover new symmetry and topological features of $\bf{g}=\bf{g}_L+\bf{g}_S$ 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 $\bf{g}_S(\bf{k})$, we prove that the scalar function $det(\bf{g}_S(\bf{k}))$ 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 $\bf{k}$ on these surfaces, the Bloch states $|u_{n\bf{k}}\rangle$ have maximal spin-orbital entanglement. Using tight-binding calculations, we observe that the surfaces $det(\bf{g}(\bf{k}))=0$ exhibit many interesting topological features, exhibiting Lifshitz critical points as understood in Fermi-surface theory.
title g-factor symmetry and topology in semiconductor band states
topic Quantum Physics
url https://arxiv.org/abs/2402.06310