Valley splitting in strained Si/SiGe quantum wells is a central parameter for silicon spin qubits and is commonly described with envelope function and effective mass theories. These models provide a computationally efficient continuum description and agree well with atomistic approaches when the confinement potential varies smoothly on the lattice scale. In modern Si/SiGe heterostructures with atomically sharp interfaces and engineered Ge concentration profiles, however, the slowly varying potential approximation underlying conventional (local) envelope function theory is challenged. We formulate an exact multivalley envelope function model by combining Burt–Foreman-type envelope function theory, which does not rely on the assumption of a slowly varying potential, with a valley-sector decomposition of the Brillouin zone. This construction enforces band-limited envelopes, which satisfy a set of coupled integro-differential equations with a nonlocal potential energy operator. Using degenerate perturbation theory, we derive the intervalley coupling matrix element within this nonlocal model and prove that it is strictly invariant under global shifts of the confinement potential (choice of reference energy). We then show that the conventional local envelope model generically violates this invariance due to spectral leakage between valley sectors, leading to an unphysical energy-reference dependence of the intervalley coupling. The resulting ambiguity is quantified by numerical simulations of various engineered Si/SiGe heterostructures. Finally, we propose a simple spectrally filtered local approximation that restores energy-reference invariance exactly and provides a good approximation to the exact nonlocal theory.

Close

PrevNext

View figure in article

• Quantum information with solid state qubits
• Valley degrees of freedom
• Layered semiconductors
• Nanostructures
• Quantum dots
• Quantum wells
• Effective mass theory