Rashba-coupling modelling for two-dimensional and high-order Rashba Hamiltonian for one-dimensional confined heavy holes

Based on standard k.p (8 x 8) multiband Hamiltonian, we have deduced an explicit analytical expression for the Rashba-coupling parameter which clarifies its anomalous behavior for heavy holes (hh), gated in quasi-two-dimensional (Q2D) systems, by letting grow the density. Our modelling remarkable better agrees with experimental results in comparison with earlier theoretical models, while recovers the expected cubic dependence on the quasi-momentum. For quasi-one-dimensional (Q1D) hh systems, we have formally derived an effective Rashba Hamiltonian with two competitive terms on the quasi-momentum, a linear term and a cubic one as predicted from suitable approximations to the Q2D scope. The Rashba-coupling parameters also behave anomalously and qualitatively support recent experiments in core/shell nanowires. Furthermore, they exhibit an essential asymptotic discontinuity in the low density regime as a function of the lateral confinement length. For hh, we present closed schemes to accurately quote the Rashba-coupling parameters both for the Q2D and Q1D systems, which become unprecedented for holes.