  The usual models for electrical spin manipulation in semiconductor quantum
dots assume that the confinement potential is separable in the three spatial
dimensions and that the AC drive field is homogeneous. However, the electric
field induced by the gates in quantum dot devices is not fully separable and
displays significant inhomogeneities. Here, we address the electrical
manipulation of hole spins in semiconductor heterostructures subject to
inhomogeneous vertical electric fields and/or in-plane AC electric fields. We
consider Ge quantum dots electrically confined in a Ge/GeSi quantum well as an
illustration. We show that the lack of separability between the vertical and
in-plane motions gives rise to an additional spin-orbit coupling mechanism
(beyond the usual linear and cubic in momentum Rashba terms) that modulates the
principal axes of the hole gyromagnetic g-matrix. This non-separability
mechanism can be of the same order of magnitude as Rashba-type interactions,
and enables spin manipulation when the magnetic field is applied in the plane
of the heterostructure even if the dot is symmetric (disk-shaped). More
generally, we show that Rabi oscillations in strongly patterned electric fields
harness a variety of g-factor modulations. We discuss the implications for the
design, modeling and understanding of hole spin qubit devices.
