Thermodynamic Evidence for a Two-Component Superconducting Order Parameter in Sr${}_2$RuO${}_4$

Abstract

Sr${}_2$RuO${}_4$ has stood as the leading candidate for a spin-triplet superconductor for 26 years. Recent NMR experiments have cast doubt on this candidacy, however, and it is difficult to find a theory of superconductivity that is consistent with all experiments. What is needed are symmetry-based experiments that can rule out broad classes of possible superconducting order parameters. Here we use resonant ultrasound spectroscopy to measure the entire symmetry-resolved elastic tensor of Sr${}_2$RuO${}_4$ through the superconducting transition. We observe a thermodynamic discontinuity in the shear elastic modulus $c_{66}$, requiring that the superconducting order parameter is two-component. A two-component $p$-wave order parameter, such as $p_x+i{p}_y$, naturally satisfies this requirement. As this order parameter appears to be precluded by recent NMR experiments, we suggest that two other two-component order parameters, namely $\left\{d_{xz},d_{yz}\right\}$ or $\left\{d_{x^2-y^2},g_{xy(x^2-y^2)}\right\}$, are now the prime candidates for the order parameter of Sr${}_2$RuO${}_4$.

References in corpus (8)

• High Resolution Polar Kerr Effect Measurements of Sr2RuO4: Evidence for Broken Time Reversal Symmetry in the Superconducting State
• Observation of half-height magnetization steps in Sr2RuO4
• Strong spin-orbit coupling effects on the Fermi surface of Sr2RuO4 and Sr2RhO4
• 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
• High sensitivity heat capacity measurements on Sr2RuO4 under uniaxial pressure
• Unsplit superconducting and time reversal symmetry breaking transitions in Sr${}_2$RuO${}_4$ under hydrostatic pressure and disorder

Cited by in corpus (94)

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• A proposal for reconciling diverse experiments on the superconducting state in Sr2RuO4
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• Evidence for even parity unconventional superconductivity in Sr${}_2$RuO${}_4$
• Elastocaloric determination of the phase diagram of 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
• Orientation-dependent Josephson effect in spin-singlet superconductor/altermagnet/spin-triplet superconductor junctions
• 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
• Theory of nematic charge orders in kagome metals
• Single-Component Superconductivity in UTe${}_2$ at Ambient Pressure
• 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
• Spectroscopic signatures of time-reversal symmetry breaking superconductivity
• Shadowed triplet pairings in Hund's metals with spin-orbit coupling
• Quasiparticle Interference of the van-Hove singularity in Sr${}_2$RuO${}_4$
• Heat capacity double transitions in time-reversal symmetry broken superconductors
• Higher angular momentum pairings in interorbital shadowed-triplet superconductors: Application to Sr${}_2$RuO${}_4$
• 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
• Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D
• Leading superconducting instabilities in three-dimensional models for Sr2RuO4
• Strain-induced time reversal breaking and half quantum vortices near a putative superconducting tetra-critical point in Sr${}_2$RuO${}_4$
• Optical Manipulation of Domains in Chiral Topological Superconductors
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• Phenomenology of bond and flux orders in kagome metals
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• Strong Magneto-Elastic Coupling in Mn${}_3$X (X = Ge, Sn)
• 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
• 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${}_4$
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• Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4
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• Enhanced Seebeck coefficient through the magnetic fluctuations in Sr${}_2$Ru${}_{1-x}{M}_x$O${}_4$ ($M=$ Co, Mn)
• Quantum-geometry-induced anomalous Hall effect in nonunitary superconductors and application to Sr${}_2$RuO${}_4$
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• Novel way to construct spatially localized finite energy structures
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• Rapid Method for Computing the Mechanical Resonances of Irregular Objects
• Symmetry Aspects of Chiral Superconductors
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• Elastic Quantum Criticality in Nematics and Altermagnets via the Elasto-Caloric Effect
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• Momentum dependent gap in holographic superconductors revisited
• Carrier filtering effect for enhanced thermopower in a body-centered tetragonal ruthenate
• Strontium Ferrite Under Pressure: Potential Analogue to Strontium Ruthenate
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• Direct evidence for the absence of coupling between shear strain and superconductivity in Sr2RuO4
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• Nematicity Arising from a Chiral Superconducting Ground State in Magic-Angle Twisted Bilayer Graphene under In-Plane Magnetic Fields
• Polar Kerr Effect in Multiband Spin-Orbit Coupled Superconductors
• Thermal fluctuations and vortex lattice structures in chiral $p$-wave superconductors: robustness of double-quanta vortices
• Why Scanning Tunneling Microscopy on Sr${}_2$RuO${}_4$ sometimes doesn't see the superconducting gap
• Multipolar Fermi Surface Deformations in Sr${}_2$RuO${}_4$ Probed by Resistivity and Sound Attenuation: A Window into Electron Viscosity and the Collision Operator
• Gor'kov-Hedin-Baym Equations for Quantum Many-Body Systems with Spin-Dependent Interactions
• Competing spin-fluctuations in Sr${}_2$RuO${}_4$ and their tuning through epitaxial strain
• Frequency-Dependent Superconducting States From the Two-Time Linear Response Theory: Application To Sr${}_2$RuO${}_4$
• Spin Fluctuations in Sr${}_{1.8}$La${}_{0.2}$RuO${}_4$
• Distinguishing $d_{xz}+i{d}_{yz}$ and $d_{x^2-y^2}$ pairing in $S{r}_{2}Ru{O}_4$ by high magnetic field H-T phase diagrams
• Examining the possibility of chiral superconductivity in Sr${}_2$RuO${}_4$ and other compounds via applied supercurrent
• Josephson effects in the spin-triplet superconductor/altermagnet/spin-triplet superconductor junctions: the detection of the intrinsic $\mathbf{d}$-vector
• Chiral topological superconductivity in twisted bilayer and double bilayer graphene
• Strain-induced Berry phase in chiral superconductors
• Ultrasonic Observation of Slowing Down of Multipole Fluctuations in Sr${}_2$RuO${}_4$
• Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems
• Anisotropic scattering rates in strain-tuned Sr${}_2$RuO${}_4$