Effective dynamics for a spin-1/2 particle constrained to a curved layer with inhomogeneous thickness

We derive an effective Hamiltonian for a spin-1/2 particle confined within a curved thin layer with non-uniform thickness using the confining potential approach. Our analysis reveals the presence of a pseudo-magnetic field and effective spin-orbit interaction (SOI) arising from the curvature, as well as an effective scalar potential resulting from variations in thickness. Importantly, we demonstrate that the physical effect of additional SOI from thickness fluctuations vanishes in low-dimensional systems, thus guaranteeing the robustness of spin interference measurements to thickness imperfection. Furthermore, we establish the applicability of the effective Hamiltonian in both symmetric and asymmetric confinement scenarios, which is crucial for its utilization in one-side etching systems.