Rashba spin-orbit coupling and nonlocal correlations in disordered 2D systems

We present an extension of the dynamical cluster approximation (DCA) that incorporates Rashba spin-orbit coupling (SOC) to investigate the interplay between disorder, spin-orbit interaction, and nonlocal spatial correlations in disordered two-dimensional systems. By analyzing the average density of states, momentum-resolved self-energy, and return probability, we demonstrate how Rashba SOC and nonlocal correlations jointly modify single-particle properties and spin-dependent interference. The method captures key features of the symplectic universality class, including SOC-induced delocalization signatures at finite times. We benchmark the DCA results against those obtained from the numerically exact kernel polynomial method, finding good agreement. This validates the computationally efficient, mean-field-based DCA framework as a robust tool for exploring disorder, spin-orbit coupling, and nonlocal correlation effects in low-dimensional systems, and paves the way for simulating multiorbital and strongly correlated systems that were previously inaccessible due to computational limitations.