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Two-dimensional hole gases in semiconductor quantum wells are promisingplatforms for spintronics and quantum computation but suffer from the lack ofthe $\bf{k}$-linear term in the Rashba spin-orbit coupling (SOC), which isessential for spin manipulations without magnetism and commonly believed to bea $\bf{k}$-cubic term as the lowest order. Here, contrary to conventionalwisdom, we uncover a strong and tunable $\bf{k}$-linear Rashba SOC intwo-dimensional hole gases (2DHG) of semiconductor quantum wells by performingatomistic pseudopotential calculations combined with an effective Hamiltonianfor a model system of Ge/Si quantum wells. Its maximal strength exceeds 120meV{\AA}, comparable to the highest values reported in narrow bandgap III-Vsemiconductor 2D electron gases, which suffers from short spin lifetime due tothe presence of nuclear spin. We also illustrate that this emergent$\bf{k}$-linear Rashba SOC is a first-order direct Rashba effect, originatingfrom a combination of heavy-hole-light-hole mixing and direct dipolarintersubband coupling to the external electric field. These findings confirmGe-based 2DHG to be an excellent platform towards large-scale quantumcomputation.

Emergence of the strong tunable linear Rashba spin-orbit coupling of two-dimensional hole gases in semiconductor quantum