Theory of valley physics in SiGe quantum dots

The weak spin-orbit coupling and the nuclear zero-spin isotopes of silicon and germanium make Si/Ge quantum dots an ideal host for semiconductor spin qubits. However, the degeneracy of the conduction band minima of bulk silicon, known as valleys, limits the performance and scalability of quantum information processing, because the valley degree of freedom competes with the spin as a low-energy two-level system. The valley degeneracy is lifted in quantum dots in Si/SiGe heterostructures due to biaxial strain and a sharp interface potential, but the reported valley splittings are often uncontrolled and can be as low as 10 to 100 μeV. This presentation will discuss in detail the main challenges for the enhancement and control of the valley splitting in silicon quantum dots. In addition, it will describe a new three-dimensional model within the effective mass theory for the calculation of the valley splitting in Si/SiGe heterostructures, which takes into account concentration fluctuations at the interface and the lateral confinement. With this model, we predicted the valley splitting as a function of various parameters, such as, the width of the interface, the electric field and the size and location of the quantum dot.