Experimental feasibility of complex-eigenvalue pairing in Sr2RuO4

Determine whether the complex-eigenvalue pairing state predicted for Sr2RuO4 is realized in the material, thereby establishing the feasibility of an intrinsically time-reversal-symmetry-breaking superconducting state with a complex gap function.

Background

The paper identifies a distinctive class of solutions to the frequency-dependent linearized Eliashberg equation with complex-conjugate eigenvalues. The associated inter-orbital gap functions have independently nonzero real and imaginary parts on the real-frequency axis and therefore break time-reversal symmetry intrinsically, without requiring a complex linear combination of degenerate order-parameter components.

Numerical calculations suggest that this pairing behavior can occur in Sr2RuO4 and is associated with strong Hund’s coupling. The authors nevertheless state that the material-specific feasibility of this pairing remains unresolved because the available experimental evidence is inconclusive. They note that observing a single-component nematic superconducting state that also breaks time-reversal symmetry could provide an unambiguous signature of the proposed complex-eigenvalue pairing.

References

While the actual feasibility of the complex eigenvalue pairing in Sr$_2$RuO$_4$ is still inconclusive with the experimental evidences at hand, this unique form of the SC pairing is worth the attention in general SC materials especially with the significant role of the Hund's coupling in the electronic correlation such as Hund's metals.

— Revised symmetry rule and intrinsically time-reversal symmetry breaking pairing in multi-orbital superconductors  (2608.22902 - Moon, 24 Aug 2026) in Conclusion, final paragraph before the Summary

We numerically compute the interference pattern to demonstrate that the magnitude and phase of the order parameter can be reconstructed as a function of angle, providing a route towards resolving the longstanding open experimental problem of directly detecting phase winding in topological superconductors.

— Imaging phase winding in topological superconductors with a fork-tip Josephson STM  (2609.38174 - Poliakov et al., 29 Sep 2026) in Abstract