Current-induced spin polarisation in Rashba-Dresselhaus systems under different point groups

Non-magnetic materials without inversion symmetry typically exhibit strong Rashba spin-orbit coupling (SOC), enabling the well-known Rashba Edelstein effect where an external electrical current induces transverse spin polarisation. In this study, we demonstrate that electrically induced spin polarisation in non-magnetic materials, for example, electronic systems within quantum-well geometries, can significantly be influenced by the system's point-group symmetries, such as $C_n$ and $C_{nv}$. These symmetries allow various linear and higher-order momentum, $k-$varying SOC Hamiltonian. Specifically, we show that surfaces having $C_{n}$ point-group symmetry, which permits specific linear and cubic Rashba and Dresselhaus SOC terms, can lead to both orthogonal and non-orthogonal spin polarisations with respect to the applied field. In contrast, surfaces with $C_{nv}$ symmetry exhibit only transverse spin polarisation, regardless of the linear and cubic SOC terms. We further find contrasting spin polarisation for cubic-in-$k$ SOC as compared to the linear-in-$k$ SOC when energy is varied, for example, through doping. Additionally, we show that the surfaces with $C_{n}$ symmetry may exhibit persistent spin current, depending on the relative strength between different momentum-dependent SOC terms. Our finding emphasizes the significance of crystal symmetry in understanding and manipulating induced spin polarisation in noncentrosymmetric materials, especially in surface/interface systems.