Effect of disorder and strain on the operation of planar Ge hole spin qubits

Germanium quantum dots in strained Ge/Si1−xGex heterostructures exhibit fast and coherent hole qubit control. Nevertheless, a full theoretical understanding of their underlying physics is lacking due to the absence of a systematic method of accounting for inhomogeneous strain, whose effects often overwhelm the bare spin-orbit coupling in the Luttinger Hamiltonian. Here we seek to remedy this shortcoming by addressing the effects of random alloy disorder and gate-induced strain on the operation of planar Ge hole spin qubits. In good agreement with experimental numbers, our hybrid approach to realistic device modeling suggests that the resultant strain inhomogeneity make a strong contribution to the linear-k spin-orbit coupling1, which is Dresselhaus-like and eventually dominates hole spin EDSR; and there exist specific in-plane B-field and and the microwave drive ( $${\tilde{{\bf{E}}}}_{{\rm{ac}}}$$ ) orientations for maximum hole spin EDSR Rabi frequency. State-of-the-art atomistic tight binding calculations via nano-electronic modeling (NEMO3D) are in agreement with the k ⋅ p description.