Theory of Valley Splitting in Si/SiGe Spin-Qubits: Interplay of Strain, Resonances and Random Alloy Disorder

Electron spin-qubits in silicon-germanium (SiGe) heterostructures are a major candidate for the realization of scalable quantum computers. A critical challenge in strained Si/SiGe quantum wells (QWs) is the existence of two nearly degenerate valley states at the conduction band minimum that can lead to leakage of quantum information. To address this issue, various strategies have been explored to enhance the valley splitting (i.e., the energy gap between the two low-energy conduction band minima), such as sharp interfaces, oscillating germanium concentrations in the QW (known as wiggle wells) and shear strain engineering. In this work, we develop a comprehensive envelope-function theory augmented by an empirical nonlocal pseudopotential model to incorporate the effects of alloy disorder, strain, and non-trivial resonances arising from interactions between valley states across neighboring Brillouin zones. We apply our model to analyze common epitaxial profiles studied in the literature with a focus on wiggle well type structures and compare our results with previous work. Our framework provides an efficient tool for quantifying the interplay of these effects on the valley splitting, enabling complex epitaxial profile optimization in future work.