Superconducting state of Sr${}_2$RuO${}_4$ in the presence of longer-range Coulomb interactions

Abstract

The symmetry of the superconducting condensate in Sr${}_2$RuO${}_4$ remains controversial after nuclear magnetic resonance (NMR) experiments recently overturned the dominant chiral $p$-wave paradigm. Several theoretical proposals have been put forward to account for existing experiments, including a $d+ig$-wave admixture, conjectured to be stabilized by longer-range Coulomb interactions. We perform a material-specific microscopic theoretical study of pairing by spin- and charge-fluctuations in Sr${}_2$RuO${}_4$, including the effects of spin-orbit coupling, and both local and longer-range Coulomb repulsion. The latter has important consequences for Sr${}_2$RuO${}_4$ due to the near-degeneracy of symmetry-distinct pairing states in this material. We find that both the $g$- and $d_{x^2-y^2}$-wave channels remain noncompetitive compared to leading nodal $s^{\prime }$, $d_{xy}$, and helical ($p$) solutions. This suggests nodal time-reversal symmetry broken $s^{\prime }+i{d}_{xy}$ or $s^{\prime }+ip$ phases, promoted by longer-range Coulomb repulsion, as the most favorable candidates for Sr${}_2$RuO${}_4$. We analyse the properties of these states, and show that the $s^{\prime }+i{d}_{xy}$ solution agrees with the bulk of available experimental data, including recent discoveries from NMR, muon spin relaxation ($\mu$SR), and ultrasound measurements.

4 pages, 2 figures + supplementary material

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• Higher angular momentum pairings in interorbital shadowed-triplet superconductors: Application to Sr${}_2$RuO${}_4$
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• Leading superconducting instabilities in three-dimensional models for Sr2RuO4
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• Spontaneous time-reversal symmetry breaking by disorder in superconductors
• Constraints on the superconducting state of Sr${}_2$RuO${}_4$ from elastocaloric measurements
• Revisiting superconductivity in the extended one-band Hubbard model: pairing via spin and charge fluctuations
• Exploring the role of nonlocal Coulomb interactions in perovskite transition metal oxides
• Emergent Tetragonality in a Fundamentally Orthorhombic Material
• Crossover between electron-electron and electron-phonon mediated pairing on the Kagome lattice
• Multiband mean-field theory of the $d+ig$ superconductivity scenario in Sr${}_2$RuO${}_4$
• Superconductivity in multiorbital systems with repulsive interactions: Hund's pairing vs. spin-fluctuation pairing
• Thermodynamic transitions and topology of spin-triplet superconductivity: Application to UTe${}_2$
• $\mu$SR measurements on Sr${}_2$RuO${}_4$ under $⟨110⟩$ uniaxial stress
• Higher angular momentum pairing states in Sr${}_2$RuO${}_4$ in the presence of longer-range interactions
• A microscopic Ginzburg--Landau theory and singlet ordering in Sr${}_2$RuO${}_4$
• Multipole-fluctuation pairing mechanism of $d_{x^2-y^2}+ig$ superconductivity in Sr${}_2$RuO${}_4$
• Strong Increase in Ultrasound Attenuation Below T${}_{\mathrm{c}}$ in Sr${}_2$RuO${}_4$: Possible Evidence for Domains
• Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4
• Spin-density wave and superconductivity in La${}_4$Ni${}_3$O${}_{10}$ under ambient pressure
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• Proximity-driven ferromagnetism and superconductivity in the triangular Rashba-Hubbard model
• Suppressed fluctuations as the origin of the static magnetic order in strained Sr${}_2$RuO${}_4$
• Enhanced Seebeck coefficient through the magnetic fluctuations in Sr${}_2$Ru${}_{1-x}{M}_x$O${}_4$ ($M=$ Co, Mn)
• A review of some new perspectives on the theory of superconducting Sr${}_2$RuO${}_4$
• Microscopic origin of ultranodal superconducting states in spin-1/2 systems
• Effects of orbital selective dynamical correlation on the spin susceptibility and superconducting symmetries in Sr${}_2$RuO${}_4$
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• Surface State of Inter-orbital Pairing State in Sr${}_2$RuO${}_4$ Superconductor
• 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${}_4$
• Evolution of Interorbital Superconductor to Intraorbital Spin-Density Wave in Layered Ruthenates
• Pairing susceptibility in the weakly interacting multilayer Hubbard model evaluated by direct perturbative expansion
• Polar Kerr Effect in Multiband Spin-Orbit Coupled Superconductors
• Probing time-reversal symmetry breaking at microwave frequencies
• Why Scanning Tunneling Microscopy on Sr${}_2$RuO${}_4$ sometimes doesn't see the superconducting gap
• Mechanism for Nodal Topological Superconductivity on PtBi${}_2$ Surface
• Topological Superconductivity in Sn/Si(111) driven by non-local Coulomb interactions