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Higher angular momentum pairing states in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">Sr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">RuO</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math> in the presence of longer-range interactions
The superconducting symmetry of ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ remains a puzzle. Time-reversal symmetry breaking ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{g}_{xy({x}^{2}\ensuremath{-}{y}^{2})}$ pairing has been proposed for reconciling multiple key experiments. However, its stability remains unclear. In this work, we theoretically study the superconducting instabilities in ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$, including the effects of spin-orbit coupling (SOC), in the presence of both local …