The intrinsic spin Hall effect (SHE) originates from spin-orbit coupling (SOC) and, featured by its low-energy dissipation, has emerged as a pivotal phenomenon with transformative potential in next-generation information technologies and quantum computing. Despite significant progress in investigating the SHE across various interaction regimes and advances in material engineering approaches, a fundamental principle governing the relationship between the intrinsic SHE and symmetry breaking remains elusive, especially in Rashba systems where spin is not a conserved quantity. Here, we employ a two-dimensional (2D) Dirac-Rashba model as a computational platform to investigate how interactions and symmetry alterations govern the SHE. We investigate the intrinsic SHE via adopting the unified theoretical framework demonstrated by Xiao et al. [Phys. Rev. B 104, L241411 (2021)], which assures a circulating spin current with null net flow at equilibrium. Three useful results are obtained: (i) even when the band spin splitting induced by SOC is strong enough, the intrinsic SHE might be absent because the Berry curvature could be missing; (ii) while Rashba SOC arises from the horizontal mirror plane symmetry $(z\to -z)$ breaking, the intrinsic SHE necessitates additional 2D inversion symmetry $\left[\right(x,y)\to (-x,-y\left)\right]$ breaking to manifest; (iii) the sign reversal of SHE is predicted by altering the symmetry breaking-induced potentials, which are controllable through vertical strain experimentally. Our results pave an insight for 2D SHE manipulation vias symmetry engineering.

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• 2-dimensional systems
• Lattice models in condensed matter
• Symmetries in condensed matter
• Tight-binding model