Possible three-dimensional nematic odd-parity superconductivity in Sr${}_2$RuO${}_4$

Abstract

The superconducting pairing in Sr${}_2$RuO${}_4$ is widely considered to be chiral $p$-wave with ${\vec{d}}_{\mathbf{k}}\sim (k_x+i{k}_y)\hat{z}$, which belongs to the $E_u$ representation of the crystalline $D_{4h}$ group. However, this superconducting order appears hard to reconcile with a number of key experiments. In this paper, based on symmetry analysis we discuss the possibility of odd-parity pairing with inherent three-dimensional (3D) character enforced by the inter-orbital interlayer coupling and the sizable spin-orbit coupling (SOC) in the material. We focus on a yet unexplored $E_u$ pairing, which contains finite $(k_z\hat{x}$, $k_z\hat{y})$-component in the gap function. Under appropriate circumstances a novel time-reversal invariant nematic pairing can be realized. This nematic superconducting state could make contact with some puzzling observations on Sr${}_2$RuO${}_4$, such as the absence of spontaneous edge current and no evidences of split transitions under uniaxial strains.

5.5pages+Supplementary. Added discussions about the absence of split transitions under uniaxial strains. Corrected an error in Supplementary

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• Superconducting Symmetries of Sr${}_2$RuO${}_4$ from First-Principles Electronic Structure
• Superconducting state of Sr${}_2$RuO${}_4$ in the presence of longer-range Coulomb interactions
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• Theory of Strain-Induced Magnetic Order and Splitting of $T_c$ and $T_{\mathrm{TRSB}}$ in Sr${}_2$RuO${}_4$
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• Leading superconducting instabilities in three-dimensional models for Sr2RuO4
• Two-Fold-Symmetric Magnetoresistance in Single Crystals of Tetragonal BiCh2-Based Superconductor LaO0.5F0.5BiSSe
• Orientational order parameters for arbitrary quantum systems
• Hidden anomalous Hall effect in Sr${}_2$RuO${}_4$ with chiral superconductivity dominated by the Ru $d_{xy}$ orbital
• Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4
• Inter-orbital p- and d-wave pairings between $d_{xz/yz}$ and $d_{xy}$ orbitals in Sr${}_2$RuO${}_4$
• A review of some new perspectives on the theory of superconducting Sr${}_2$RuO${}_4$
• Quantum-geometry-induced anomalous Hall effect in nonunitary superconductors and application to Sr${}_2$RuO${}_4$
• Degeneracy between even- and odd-parity superconductivity in the quasi-1D Hubbard model and implications for Sr2RuO4
• Possible two-component spin-singlet pairings in Sr2RuO4
• High-pressure synthesis of Ba${}_2$RhO${}_4$, a rhodate analogue of the layered perovskite Sr-ruthenate
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