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arXiv:2505.00806 · SciPost Physics

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

Ying Li, Gour Jana, Chinedu E. Ekuma

Published Nov 24, 2025• 0 citations
arXivHTMLPDF

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.

DOI
10.21468/scipostphys.19.5.135

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Abstract The interplay between spin-orbit coupling (SOC) and nearest-neighbor (NN) repulsion in optical lattices provides a fertile ground for realizing exotic quantum phases that simultaneously host finite-momentum condensation and spontaneous density modulation. We address this interplay for spin-1 bosons in a two-dimensional square lattice with Rashba SOC and NN interactions, employing the single-site Gutzwiller mean-field (SGMF) method as our primary tool and the 2×22\times22×2 cluster Gutzwiller mean-field (CGMF) approach as a systematic check of short-range correlation effects. Our central finding is that SOC fundamentally reconstructs the single-particle band structure, shifting the lowest-band minimum from zero to finite momenta with increasing SOC strength. This reconstruction underpins a cascade of modulated superfluid (SF) phases-stripe, square, twist, and checkerboard-whose condensate textures are dictated predominantly by SOC. The addition of NN repulsion naturally favors real-space density ordering; the competition and cooperation between this density order and SOC-generated phase textures then stabilize a family of supersolid (SS) phases that mirror the same four modulated patterns, in which finite-momentum condensate and density-wave orders coexist. To complement the numerical phase diagrams, we derive semi-analytical phase boundaries for both the Mott-insulator (MI)-SF and density-wave (DW)-SS transitions using second-order perturbation theory. These expressions not only reproduce the overall trends of the SGMF results but also provide a transparent physical picture of the underlying instability mechanisms. Importantly, the representative CGMF calculations retain the same DW lobes and intervening SS regions, albeit with quantitative shifts, while systematic finite-size analyses reveal only weak dependence on lattice size, with no evidence of phase separation, collectively attesting to the robustness of the predicted phase structure. Together, our results establish a comprehensive mean-field framework that unifies the SOC-driven finite-momentum condensation and the NN-interaction-induced density ordering within a single picture, offering a valuable benchmark for future experimental explorations of spin-orbit-coupled spinor gases in optical lattices.
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