Spin textures and Larmor precession of holes modulated by the spin-orbit coupling confined in the two-dimensional Si x Ge 1-x mixed-alloy quantum well system

We theoretically study the spin textures of holes confined in the two-dimensional (2D) [Formula: see text] quantum well (QW) system. We particularly focus on the spin-orbit interaction (SOI) caused by the bulk-inversion-asymmetry (BIA) and explore the effective magnetic field (EMF) generated by the combination of the SOI couplings. For the study of the semiconductor mixed-alloy (MA) system, we propose the extended [Formula: see text] perturbation approach including possible perturbation terms crossing with the SOI couplings up to the second order ones. We then study the distribution and orientation of the EMF and investigate how the EMF changes the spin textures of the heavy-mass holes (HHs), light-mass holes (LHs) and separated holes (SHs), respectively. Finally, we study the Larmor spin precession of these holes having the characteristic spin textures driven by the SOI couplings.