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
Xin Wang, Zhiqiang Wang, Catherine Kallin
Abstract
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 and longer-range interactions within a random-phase approximation. We show that the inclusion of second-nearest-neighbor repulsions, together with nonlocal SOC in the ${B}_{2g}$ channel or orbital-anisotropy of the nonlocal interactions, can have a significant impact on the stability of both ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$- and $g$-wave pairing channels. We analyze the properties, such as Knight shift and spontaneous edge current, of the realized ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+ig, {s}^{\ensuremath{'}}+i{d}_{xy}$, and mixed helical pairings in different parameter spaces, and we find that the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+ig$ solution is in better agreement with the experimental data.