Superconductivity in Correlated Multi-Orbital Systems with Spin-Orbit Coupling: Coexistence of Even- and Odd-Frequency Pairing and the Case of Strontium Ruthenate

• Published in: arXiv.org 2022-08
• Main Authors: Gingras, Olivier, Allaglo, Nikita, Nourafkan, Reza, Côté, Michel, Tremblay, André-Marie S
• Format: Article
• Language: English
• Subjects: Correlation; Density functional theory; Entanglement; Group theory; Order parameters; Phase diagrams; Quantum numbers; Spin-orbit interactions; Strontium ruthenium oxide; Superconductivity; Temperature dependence
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2201.08918

The superconducting order parameter of strontium ruthenate is the center of a lasting puzzle calling for theoretical studies that include the seldom-considered effects of spin-orbit coupling and the frequency-dependence of the order parameters. Here we generalize the frequency-dependent theory of superconductivity mediated by spin and charge fluctuations to include spin-orbit coupling in multi-orbital systems and we characterize the superconducting states using the spin-parity-orbital-time \(SPOT\) quantum numbers, group theory, and phase distributions in the complex plane. We derive a pseudospin formulation that maps the inter-pseudospin sector of the normal state Eliashberg equation to a pseudospin-diagonal one. Possible superconducting order parameters for strontium ruthenate are obtained starting from a realistic density-functional-theory normal state. We find that spin-orbit coupling leads to ubiquitous entanglement of spin and orbital quantum numbers, along with notable mixing between even- and odd-frequency correlations. We propose a phase diagram obtained from the temperature dependence of the leading and subleading symmetries in the pseudospin-orbital basis. An accidental degeneracy between leading inter-pseudospin symmetries in strontium ruthenate, B\(_{1g}^+\) and A\(_{2g}^-\), could resolve apparent experimental contradictions.