Rashba Spin-Orbit Coupling and Nonlocal Correlations in Disordered 2D Systems

TL;DR

The paper extends the dynamical cluster approximation to include Rashba spin–orbit coupling, enabling a nonlocal mean-field study of disorder and SOC in 2D systems. By analyzing the average density of states, momentum-resolved self-energy, and return probability, it demonstrates SOC-induced delocalization effects and the crucial role of nonlocal correlations in shaping spin-dependent interference within the symplectic universality class. The extended DCA–SOC approach aligns well with numerically exact kernel polynomial method results, validating its accuracy and efficiency for exploring disordered, spin–orbit-coupled systems and paving the way for future multiorbital and strongly correlated extensions. However, like other mean-field methods, it cannot capture the Anderson localization transition itself, motivating future incorporation of typical-medium extensions (TMDCA) for ALT physics and transport studies.

Abstract

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.

Figures (4)

• Figure 1: ADOS computed using DCA for disordered two-dimensional electronic systems without Rashba SOC (left panels) and with SOC at $\alpha = 0.25$ (right panels). Panels (a)–(f) compare results for $N_c = 1$ (CPA, black solid curves), $N_c = 18$ (green dot-dashed curves) and $N_c = 32$ (red dashed curves) at increasing disorder strengths: $W = 0.20$ ((a), (b)), $W = 0.50$ ((c), (d)), and $W = 1.00$ ((e), (f)).
• Figure 2: Imaginary part of the self-energy, $\mathrm{Im}\,\underline{\Sigma}(\vb{K}, \omega))$, computed using DCA for disordered two-dimensional systems without Rashba SOC (left panels) and with SOC at $\alpha = 0.25$ (right panels). Panels (a) and (b) show results for weak disorder ($W = 0.20$) at $N_c = 1$ (CPA) and $N_c = 32$, evaluated at high-symmetry momenta $\vb{K} = (0,0)$, $(\pi,0)$, and $(\pi,\pi)$. Panels (c) and (d) show the corresponding results at stronger disorder ($W = 0.80$).
• Figure 3: Return probability $P(t)$ as a function of time. (a) Results at fixed disorder strength $W = 0.50$ for cluster sizes $N_{c} = 1$ (black), $N_{c} = 8$ (red), $N_{c} = 18$ (green), and $N_{c} = 32$ (blue), shown with Rashba SOC ($\alpha = 0.25$, solid curves) and without SOC ($\alpha = 0$, dashed curves). (b) Return probability for fixed cluster size $N_{c} = 32$ at $W = 0.10$ (black), $W = 0.50$ (red), and $W = 1.00$ (green), again comparing cases with (solid) and without (dashed) SOC. The inset shows the extrapolated infinite-time value $P(t \rightarrow \infty) = p(\eta \rightarrow 0)$.
• Figure 4: Benchmarking of ADOS computed using DCA for cluster sizes $N_{c} = 1$ and $N_{c} = 32$ against results obtained from the KPM for disordered two-dimensional systems with Rashba SOC ($\alpha = 0.25$) at various disorder strengths. KPM calculations were performed on a $300 \times 300$ square lattice with periodic boundary conditions using 1024 Chebyshev moments and $10^3$ disorder realizations for statistical averaging.