The pairing symmetry of Sr₂RuO₄ is a long-standing fundamental question in the physics of superconducting materials with strong electronic correlations. We use the functional renormalization group to investigate the behavior of superconductivity under uniaxial strain in a two-dimensional realistic model of Sr₂RuO₄ obtained with density functional theory and incorporating the effect of spin-orbit coupling. We find a dominant \({d}_{{{{{\rm{x}}}}}^{2}-{{{{\rm{y}}}}}^{2}}\) superconductor mostly hosted by the d_xy-orbital, with no other closely competing superconducting state. Within this framework, we reproduce the experimentally observed enhancement of the critical temperature under strain and propose a simple mechanism driven by the density of states to explain our findings. We also investigate the competition between superconductivity and spin-density wave ordering as a function of interaction strength. By comparing theory and experiment, we discuss constraints on a possible degenerate partner of the \({d}_{{{{{\rm{x}}}}}^{2}-{{{{\rm{y}}}}}^{2}}\) superconducting state.

Sr ₂ RuO ₄ 的配对对称性是强电子关联超导材料物理学中长期存在的基本问题。我们使用泛函重正化群研究了单轴应变下超导行为在二维真实模型中的 Sr ₂ RuO ₄ 通过密度泛函理论获得并结合了自旋效应-轨道耦合。我们发现了一个占主导地位的 \({d}_{{{{{\rm{x}}}}}^{2}-{{{{\rm{y}}}}}^{2}}\) 超导体主要由 d _xy 轨道托管，没有其他紧密竞争的超导态。在这个框架内，我们重现了实验观察到的应变下临界温度的增强，并提出了一种由态密度驱动的简单机制来解释我们的发现。我们还研究了超导性和自旋密度波序之间的竞争作为相互作用强度的函数。通过比较理论和实验，我们讨论了对 \({d}_{{{{{\rm{x}}}}}^{2}-{{{{\rm{y} }}}}^{2}}\) 超导态。