Typical Medium Cluster Study of Anderson Localization and Spin–Orbit–Coupled Spin Dynamics in 2D Systems

Two-dimensional (2D) disordered systems with spin-orbit coupling (SOC) belong to the symplectic universality class, where Anderson localization transitions can occur. To investigate the interplay of disorder, Rashba-type SOC, and spatial correlations, we previously extended the Typical Medium Dynamical Cluster Approximation (TMDCA) to include Rashba SOC and characterized single-particle properties such as the typical density of states. Here, we present new results based on finite-size scaling, from which we extract the critical parameters of the Anderson transition in the 2D symplectic class. We further compute spin-relaxation times and related spintronic quantities, made accessible through the inclusion of SOC. Finally, by incorporating Hubbard interactions within second-order perturbation theory, we establish a framework for exploring the combined effects of disorder, SOC, and strong correlations in 2D systems.