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Our recent study [Phys. Rev. B 103, 085309 (2021)] verified the existence of$\bf{k}$-linear Rashba spin-orbit coupling (SOC) of two-dimensional hole gasesin quantum wells (QWs) which originates from a combination ofheavy-hole-light-hole (HH-LH) mixing and direct dipolar coupling to theexternal electric field. However, the Rashba SOC dependence on QW orientationsremains unclear. Here, we explore this dependence on QW orientations anduncover an upper and lower bound to the orientation-dependent $\bf{k}$-linearRashba SOC along the [110]- and [111]- crystalline directions by performingatomistic pseudopotential calculations associated with theoretical analysis.The intrinsic HH-LH mixing at the Brillouin zone center, maximal in[110]-oriented quantum wells and minimal in [111]- and [001]-oriented QWs,plays an essential role. Remarkably, we find that only $\bf{k}$-cubic RashbaSOC exists in [111]-oriented QWs. These findings help understand the physicalmechanism of the Rashba SOC dependence on QW orientations and provide astrategic prediction for experiments to realize the large Rashba SOC.

An upper and lower bound to the orientation-dependent linear Rashba spin-orbit coupling of two-dimensional hole gases in semiconductor quantum wells