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

Two-dimensional hole gases (2DHGs) in semiconductor quantum wells are promising platforms for spintronics and quantum computation, but suffer from the lack of the $\mathbf{k}$-linear term in the Rashba spin-orbit coupling (SOC), which is essential for spin manipulations without magnetism. The Rashba SOC in 2DHGs is commonly believed to be a $\mathbf{k}$-cubic term as the lowest order. Here, contrary to conventional wisdom, we taking Ge/Si system as an example uncover a strong and tunable $\mathbf{k}$-linear Rashba SOC in 2DHGs of semiconductor quantum wells (QWs) by performing atomistic pseudopotential calculations in conjunction with theoretical analysis based on the effective model Hamiltonian approach. We illustrate that this emergent $\mathbf{k}$-linear Rashba SOC is a first-order direct Rashba effect, originating from a combination of heavy-hole-light-hole mixing and direct dipolar coupling to the external electric field. The enhanced interband mixing renders [110]-oriented Ge/Si QWs a much stronger linear Rashba SOC than [001]-oriented counterpart with the maximal strength exceeding 120 meV\AA{}, comparable to the highest values reported in two-dimensional electron gases made by narrow band-gap III-V semiconductors, which suffers from short spin lifetime due to the presence of nuclear spin. These findings confirm Ge-based 2DHGs to be an excellent platform for large-scale quantum computation.