Valley splittings in the two bands k·p model for Si/SiGe heterostructures and spin qubit

A crucial challenge for operating electron spin qubits in Si/SiGe heterostructures is to systematically achieve sufficiently large splitting between Si valleys. The most accurate methods to calculate valley splittings in Si/SiGe heterostructures are atomistic descriptions, such as tight-binding (TB) models. However, their high computational cost makes them unsuitable for realistic large-scale devices. Continuous medium approximations, such as the effective mass equations, are more practical in this context. However, the description of valley splittings, valley–orbit mixing, and intervalley dipole matrix elements in such models calls for specific refinements.

In our work, we discuss the two-bands k·p model for the conduction bands of Si, an extension of the effective mass equations that couples opposite valleys. We further extend this model by implementing inter-valley potentials. We show that it reproduces the TB valley splittings in relevant Si/SiGe heterostrucures at a much lower computational cost, while also capturing valley-orbit mixing and finite inter-valley dipole matrix elements. As such, our model enables the description of manipulation, dephasing and relaxation in spin and valley qubits. Building on these results we illustrate the relevance of the two-bands k·p model by simulating a realistic electron Si/SiGe spin qubit device. This work opens new opportunities for the understanding and optimization of Si-based electron spin qubits.