  The selective confinement of light holes (LHs) in a tensile-strained
germanium (Ge) quantum well is studied by mapping the electronic structure of
Ge$_{1-x}$Sn$_x$/Ge/Ge$_{1-x}$Sn$_x$ heterostructures as a function of Sn
content, residual strain, and Ge well thickness. It is shown that above
$12\,\text{at.}\%$ Sn and below $0.4\%$ residual compressive strain in the
barriers, the tensile strain in Ge becomes sufficiently large to yield a
valence band edge with LH-like character, thus forming a quasi two-dimensional
LH gas in Ge. The LH ground state has a larger in-plane effective mass than
that of heavy holes (HHs) in Si$_{1-y}$Ge$_y$/Ge/Si$_{1-y}$Ge$_y$ quantum
wells. Moreover, LHs in optimal Ge$_{1-x}$Sn$_x$/Ge/Ge$_{1-x}$Sn$_x$
heterostructures are found to exhibit a strong $g$-tensor anisotropy, with the
in-plane component one order of magnitude larger than that of HHs in typical
planar systems. Two of three structure-inversion-asymmetry Rashba parameters,
both of which are critical in electric-dipole-spin-resonance experiments, are
effectively 10 times the size of the cubic Rashba parameter in HH quantum
wells. In the regime of LH selective confinement, every layer of the
heterostructure is of direct bandgap, which can be relevant for efficient
optical photon-spin qubit interfaces. This work discusses the broad landscape
of the characteristics of LH spin confined in Ge to guide the design and
implementation of LH spin-based devices.
