Light-hole spin confined in germanium

The selective confinement of light holes (LHs) in a tensile-strained germanium (Ge) quantum well is studied by mapping the electronic structure of ${\mathrm{Ge}}_{1\ensuremath{-}x}{\mathrm{Sn}}_x/\mathrm{Ge}/{\mathrm{Ge}}_{1\ensuremath{-}x}{\mathrm{Sn}}_x$ heterostructures as a function of Sn content, residual strain, and Ge well thickness. It is shown that above $12\phantom{\rule{0.16em}{0ex}}\text{at.}%$ 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 ${\mathrm{Si}}_{1\ensuremath{-}y}{\mathrm{Ge}}_y/\mathrm{Ge}/{\mathrm{Si}}_{1\ensuremath{-}y}{\mathrm{Ge}}_y$ quantum wells. Moreover, LHs in optimal ${\mathrm{Ge}}_{1\ensuremath{-}x}{\mathrm{Sn}}_x/\mathrm{Ge}/{\mathrm{Ge}}_{1\ensuremath{-}x}{\mathrm{Sn}}_x$ 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.