  We investigate the existence of linear-in-momentum spin-orbit interactions in
the valence band of Ge/GeSi heterostructures using an atomistic tight-binding
method. We show that symmetry breaking at the Ge/GeSi interfaces gives rise to
a linear Dresselhaus-type interaction for heavy-holes. This interaction results
from the heavy-hole/light-hole mixings induced by the interfaces and can be
captured by a suitable correction to the minimal Luttinger-Kohn, four bands
$\vec{k}\cdot\vec{p}$ Hamiltonian. It is dependent on the steepness of the
Ge/GeSi interfaces, and is suppressed if interdiffusion is strong enough.
Besides the Dresselhaus interaction, the Ge/GeSi interfaces also make a
contribution to the in-plane gyromagnetic $g$-factors of the holes. The
tight-binding calculations also highlight the existence of a small linear
Rashba interaction resulting from the couplings between the
heavy-hole/light-hole manifold and the conduction band enabled by the low
structural symmetry of Ge/GeSi heterostructures. These interactions can be
leveraged to drive the hole spin. The linear Dresselhaus interaction may, in
particular, dominate the physics of the devices for out-of-plane magnetic
fields. When the magnetic field lies in-plane, it is, however, usually far less
efficient than the $g$-tensor modulation mechanisms arising from the motion of
the dot in non-separable, inhomogeneous electric fields and strains.
