Electric field-tuneable crossing of hole Zeeman splitting and orbital gaps in compressively strained germanium semiconductor on silicon

With the emergence of the quantum computing era, the spin physics of engineered semiconductor materials with large and tuneable effective g*-factor, which is a measure of the interaction between the magnetic field and the spin of the particle, has become of great interest because it offers new physics and engineering tools for spin's manipulation and its addressable control. Here we suggest a semi-empirical method to determine out of plane effective g*-factor in high mobility 2D hole heterostructures. We experimentally study the electric-field tuneablity of effective g*-factor of holes in a strained germanium quantum well heterostructure. As a result of the material's engineering, the g*-factor can be tuned in a large range from 13 to 24 that corresponds to the tuneable Zeeman spin splitting of heavy holes in the range from smaller, to equal, and to larger than the orbital Landau level quantization gap. Tuning the effective g-factor of semiconductors by a perpendicular electric field is essential for designing controllable spin-based devices such as qubits and spin field-effect transistors. Here, a wide-range g-factor tunability by external electric field is demonstrated in a high-mobility 2D hole heterostructure.