Quantum Steering and Nonlocal Correlations Between Non-Interacting Delocalized Electrons Under Rashba Spin-Orbit Interaction

We investigate quantum steering and nonlocal correlations between two electrons in a two-dimensional electron gas (2DEG) as functions of Rashba spin-orbit interaction (RSOI) strength and inter-electron separation. We focus particularly on the Bi/Ag(111) system characterized by its strong RSOI ($\alpha_0 = 3.05\times10^{-11}$ eV~m), and we explore the influence of tuning intensity of RSOI and inter-electron distance on the dynamics of Bell nonlocality, uncertainty-induced nonlocality and steering. We find that, although increasing $\alpha_R$ initially suppresses quantum correlations, all three metrics exhibit a non-monotonic recovery as functions of $\alpha_R$, peaking near an optimal coupling strength $\alpha_R = 4.32\times10^{-11}$~eV~m across the range of inter-electron separations considered. This finding establishes RSOI as a critical control parameter for stabilizing quantum properties in two-dimensional electron gases against the decay of quantum correlations with inter-electron separation, and shows that the suppression and recovery of quantum resources within the Bi/Ag(111) system can be controlled by adjusting the inter-electron distance and carefully tuning the RSOI strength.