Understanding the $g$-factor physics of Si/SiGe quantum dots is crucial for realizing high-quality spin qubits. While previous work has explained some aspects of $g$-factor physics in idealized geometries, the results do not extend to general cases and they miss several important features. Here, we construct a theory that gives $g$ in terms of readily computable matrix elements, and can be applied to all Si/SiGe heterostructures of current interest. As a concrete example, which currently has no $g$-factor understanding, we study the so-called wiggle well structure, containing Ge concentration oscillations inside the quantum well. Here we find a significant renormalization of the $g$ factor compared to conventional Si/SiGe quantum wells. We also uncover a giant $g$-factor suppression of order $\mathcal{O}(1)$, which arises due to spin-valley coupling, and occurs at locations of low valley splitting. Our work therefore opens up new avenues for $g$-factor engineering in Si/SiGe quantum dots.

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• Spin-orbit coupling
• Valley degrees of freedom
• Quantum dots
• Quantum wells
• Semiconductors
• k dot p method