Abstract

The g factor of electrons and holes in crystals and heterostructures of silicon, germanium, gallium arsenide, etc., is a key parameter in designing spin qubits. I will begin by discussing two different but interrelated definitions of the g factor. Authors have disagreed from the beginning about whether or not g is a symmetric second-rank tensor. I will discuss that g, which is specific to each eigenstate, whether extended or localized, is best discussed in terms of three singular values associated with eigendirections, with a separate discussion about its sign. Luttinger gave a correct formula for the g factors of band electrons, including the orbital contributions arising from the spin-orbit interaction. But it was not until fifty years later, with the advent of Berry-curvature concepts, that his formula could be given a clear physical interpretation. I will show results of a survey we have done of band g factors in silicon and germanium, emphasizing new topological aspects. It is interesting that even silicon, with its very weak spin-orbit interaction, can, because of a combination of topology and symmetry, exhibit g factors very far from 2.

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