Stabilizing Even-Parity Chiral Superconductivity in Sr${}_2$RuO${}_4$

Abstract

Strontium ruthenate (Sr${}_2$RuO${}_4$) has long been thought to host a spin-triplet chiral $p$-wave superconducting state. However, the singletlike response observed in recent spin-susceptibility measurements casts serious doubts on this pairing state. Together with the evidence for broken time-reversal symmetry and a jump in the shear modulus $c_{66}$ at the superconducting transition temperature, the available experiments point towards an even-parity chiral superconductor with $k_z(k_x\pm i{k}_y)$-like $E_g$ symmetry, which has consistently been dismissed based on the quasi-two-dimensional electronic structure of Sr${}_2$RuO${}_4$. Here, we show how the orbital degree of freedom can encode the two-component nature of the $E_g$ order parameter, allowing for a local orbital-antisymmetric spin-triplet state that can be stabilized by on-site Hund's coupling. We find that this exotic $E_g$ state can be energetically stable once a complete, realistic three-dimensional model is considered, within which momentum-dependent spin-orbit coupling terms are key. This state naturally gives rise to Bogoliubov Fermi surfaces.

6+10 pages, 5 figures

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• Ultrasound evidence for a two-component superconducting order parameter in Sr${}_2$RuO${}_4$
• A proposal for reconciling diverse experiments on the superconducting state in Sr2RuO4
• Momentum Resolved Superconducting Energy Gaps of Sr${}_2$RuO${}_4$ from Quasiparticle Interference Imaging
• Evidence for even parity unconventional superconductivity in Sr${}_2$RuO${}_4$
• High sensitivity heat capacity measurements on Sr2RuO4 under uniaxial pressure
• Reduction of the spin susceptibility in the superconducting state of Sr2RuO4 observed by polarized neutron scattering
• Unsplit superconducting and time reversal symmetry breaking transitions in Sr${}_2$RuO${}_4$ under hydrostatic pressure and disorder
• Inhomogeneous time-reversal symmetry breaking in ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$
• Superconducting state of Sr${}_2$RuO${}_4$ in the presence of longer-range Coulomb interactions
• Two scenarios for superconductivity in CeRh${}_2$As${}_2$
• Triplet Superconductivity from Nonlocal Coulomb Repulsion in an Atomic Sn Layer Deposited onto a Si(111) Substrate
• The Superconductivity of Sr${}_2$RuO${}_4$ Under $c$-Axis Uniaxial Stress
• Theory of Strain-Induced Magnetic Order and Splitting of $T_c$ and $T_{\mathrm{TRSB}}$ in Sr${}_2$RuO${}_4$
• Magic angles and correlations in twisted nodal superconductors
• Chiral singlet superconductivity in the weakly correlated metal LaPt3P
• Parity transition of spin-singlet superconductivity using sub-lattice degrees of freedom
• Shadowed triplet pairings in Hund's metals with spin-orbit coupling
• Heat capacity double transitions in time-reversal symmetry broken superconductors
• Higher angular momentum pairings in interorbital shadowed-triplet superconductors: Application to Sr${}_2$RuO${}_4$
• Inter-orbital singlet pairing in Sr${}_2$RuO${}_4$: a Hund's superconductor
• Superconductivity in Correlated Multi-Orbital Systems with Spin-Orbit Coupling: Coexistence of Even- and Odd-Frequency Pairing and the Case of Strontium Ruthenate
• Spin-orbit coupled superconductivity: Rashba-Hubbard model on the square lattice
• Leading superconducting instabilities in three-dimensional models for Sr2RuO4
• Symmetry, nodal structure, and Bogoliubov Fermi surfaces for nonlocal pairing
• Distinct reduction of Knight shift in superconducting state of Sr${}_2$RuO${}_4$ under uniaxial strain
• Spontaneous superconducting diode effect in non-magnetic Nb/Ru/Sr${}_2$RuO${}_4$ topological junctions
• Nonunitary Superconductivity in Complex Quantum Materials
• Constraints on the superconducting state of Sr${}_2$RuO${}_4$ from elastocaloric measurements
• Origin of the anomalous Hall effect in two-band chiral superconductors
• Neutron scattering studies on spin fluctuations in Sr${}_2$RuO${}_4$
• In-plane magnetic penetration depth in Sr${}_2$RuO${}_4$: muon-spin rotation/relaxation study
• Multiband mean-field theory of the $d+ig$ superconductivity scenario in Sr${}_2$RuO${}_4$
• Destruction of surface states of ($d_{zx}+i{d}_{yz}$)-wave superconductor by surface roughness: application to Sr${}_2$RuO${}_4$
• Linear optical response from the odd parity Bardasis-Schrieffer mode in locally non-centrosymmetric superconductors
• Distortional weak-coupling instability of Bogoliubov Fermi surfaces
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• Hidden anomalous Hall effect in Sr${}_2$RuO${}_4$ with chiral superconductivity dominated by the Ru $d_{xy}$ orbital
• $\mu$SR measurements on Sr${}_2$RuO${}_4$ under $⟨110⟩$ uniaxial stress
• Superconductivity in multiorbital systems with repulsive interactions: Hund's pairing vs. spin-fluctuation pairing
• A microscopic Ginzburg--Landau theory and singlet ordering in Sr${}_2$RuO${}_4$
• Using Disorder to Identify Bogoliubov Fermi-Surface States
• Magnetically-textured superconductivity in elemental Rhenium
• 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
• Spin susceptibility for orbital-singlet Cooper pair in the three-dimensional Sr${}_2$RuO${}_4$ superconductor
• Robust and tunable coreless vortices and fractional vortices in chiral $d$-wave superconductors
• Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4
• Possibility of mixed helical p-wave pairings in Sr${}_2$RuO${}_4$
• Enhanced Seebeck coefficient through the magnetic fluctuations in Sr${}_2$Ru${}_{1-x}{M}_x$O${}_4$ ($M=$ Co, Mn)
• Suppressed fluctuations as the origin of the static magnetic order in strained Sr${}_2$RuO${}_4$
• Electronic structure correspondence of singlet-triplet scale separation in strained Sr2RuO4
• Degeneracy between even- and odd-parity superconductivity in the quasi-1D Hubbard model and implications for Sr2RuO4
• Surface density of states and tunneling spectroscopy of a spin-3/2 superconductor with Bogoliubov Fermi Surfaces
• Conditions for orbital selective altermagnetism in Sr${}_2$RuO${}_4$: tight binding model, similarities with cuprates and implications on superconductivity
• Inverse Proximity Effects at Spin-Triplet Superconductor-Ferromagnet Interface
• A review of some new perspectives on the theory of superconducting Sr${}_2$RuO${}_4$
• Nodal gaps from local interactions in Sr${}_2$RuO${}_4$
• Robustness of chiral surface current and subdominant $s$-wave Cooper pairs
• Stability of Bogoliubov Fermi Surfaces within BCS Theory
• Pair-breaking in superconductors with strong spin-orbit coupling
• Possible two-component spin-singlet pairings in Sr2RuO4
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• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects
• Impurity induced double transitions for accidentally degenerate unconventional pairing states
• Impurity effect on Bogoliubov Fermi surfaces: Analysis based on iron-based superconductors
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• Spin conductance in SNN junctions with non-centrosymmetric superconductors
• Enhanced Spin-Orbit Coupling in a Correlated Metal
• Reconciling $\pi$ phase shift in Josephson junction experiments with even-parity superconductivity in Sr${}_2$RuO${}_4$
• Evolution of Interorbital Superconductor to Intraorbital Spin-Density Wave in Layered Ruthenates
• Symmetry Aspects of Chiral Superconductors
• Nonlocal electrodynamics and the penetration depth of superconducting Sr${}_2$RuO${}_4$
• Vortex supercurrent inversion by frequency-symmetry conversion of Cooper pairs
• Muon Knight shift as a precise probe of the superconducting symmetry of Sr${}_2$RuO${}_4$
• Chiral superfluid helium-3 in the quasi-two-dimensional limit
• Finite-momentum and field-induced pairings in orbital-singlet spin-triplet superconductors
• Competing spin-fluctuations in Sr${}_2$RuO${}_4$ and their tuning through epitaxial strain
• Odd-frequency pairing of Bogoliubov quasiparticles in superconductor junction
• Why Scanning Tunneling Microscopy on Sr${}_2$RuO${}_4$ sometimes doesn't see the superconducting gap
• Phenomenological model for the third-harmonic magnetic response of superconductors: application to Sr${}_2$RuO${}_4$
• Spin Fluctuations in Sr${}_{1.8}$La${}_{0.2}$RuO${}_4$
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• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors
• Chiral Current Inversion Induced by Flat-Band Andreev Bound States
• Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems
• Efficient slave-boson approach for multiorbital two-particle response functions and superconductivity