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

Abstract

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.

30 pages, 17 figures

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Cited by in corpus (18)

• Altermagnetism and superconductivity in a multiorbital t-J model
• Constraints on the superconducting state of Sr${}_2$RuO${}_4$ from elastocaloric measurements
• Distinct spin and orbital dynamics in Sr${}_2$RuO${}_4$
• Multiband mean-field theory of the $d+ig$ superconductivity scenario in Sr${}_2$RuO${}_4$
• Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4
• Suppressed fluctuations as the origin of the static magnetic order in strained Sr${}_2$RuO${}_4$
• Conditions for orbital selective altermagnetism in Sr${}_2$RuO${}_4$: tight binding model, similarities with cuprates and implications on superconductivity
• Effects of orbital selective dynamical correlation on the spin susceptibility and superconducting symmetries in Sr${}_2$RuO${}_4$
• Magic angle of Sr${}_2$RuO${}_4$: Optimizing correlation-driven superconductivity
• Strain-induced superconductivity in Sr2IrO4
• Reconciling $\pi$ phase shift in Josephson junction experiments with even-parity superconductivity in Sr${}_2$RuO${}_4$
• Nonlocal electrodynamics and the penetration depth of superconducting Sr${}_2$RuO${}_4$
• Strontium Ferrite Under Pressure: Potential Analogue to Strontium Ruthenate
• Finite-momentum and field-induced pairings in orbital-singlet spin-triplet superconductors
• Polar Kerr Effect in Multiband Spin-Orbit Coupled Superconductors
• Meissner effect in non-Hermitian superconductors
• Frequency-Dependent Superconducting States From the Two-Time Linear Response Theory: Application To Sr${}_2$RuO${}_4$
• Competing spin-fluctuations in Sr${}_2$RuO${}_4$ and their tuning through epitaxial strain