Possible three-dimensional nematic odd-parity pairing in Sr$_2$RuO$_4$ evidenced by uniaxial strain measurements

In the presence of a nontrivial three-dimensional (3D) spin-orbital entanglement, the $E_u$ superconducting pairing in Sr$_2$RuO$_4$ is inherently 3D, consisting both in-plane and out-of-plane channels: $(k_x,k_y)\hat{z}$ and $(k_z\hat{x},k_z\hat{y})$. When the latter dominates, the system may develop a time-reversal invariant nematic pairing. We show that, as the out-of-plane pairing lacks a linear-order coupling to certain symmetry-lowering perturbations such as in-plane uniaxial strains, the nematic state may observe a superconducting $T_c$ enhancement indistinguishable from a quadratic function of the strain. Further, in contrast with the chiral pairing, the nematic pairing shall exhibit only a single phase transition or a comparatively less robust secondary transition under the stated perturbations. In combine these may be consistent with several recent experiments on uniaxially-strained samples of Sr$_2$RuO$_4$, thereby providing stronger support for the 3D nematic $p$-wave pairing in this material.

Refs: [1] W. Huang and H. Yao, Phys. Rev. Lett. 121, 157002 (2018); [2] W. Huang, Y. Zhou and H. Yao, in preparation.