Boundary conditions for a hole spin qubit in a Ge quantum dot

Hole spin in a semiconductor quantum dot is an intriguing candidate for qubit because of its strong intrinsic spin-orbit coupling, which enables fast electrical control and thus potential scalability. However, hole spin qubits are more complicated than conduction electron spin qubits because of the strong mixing of heavy and light holes, and a multi-band theory is required to study hole spins accurately.



One main difficulty of studying holes in a realistic heterostructure is the coupled boundary conditions, which are a direct result of the multi-band theory. In this talk, we will introduce a perturbative treatment to address this boundary condition problem. We study a planar quantum dot in a SiGe-Ge quantum well within the formalism of effective-mass approximation, and examine how the choice of boundary conditions affect the splitting of hole spins.