Hidden quasi one-dimensional superconductivity in Sr$_2$RuO$_4$

TL;DR

This paper demonstrates that Sr$_2$RuO$_4$ exhibits triplet superconductivity originating from quasi-one-dimensional bands, characterized by a topologically trivial state with weakly pinned d-vector and no robust edge modes, explaining experimental observations.

Contribution

The study provides an asymptotically exact weak coupling analysis showing triplet pairing in Sr$_2$RuO$_4$ driven by spin and charge fluctuations, revealing its trivial topological nature.

Findings

Triplet pairing originates in quasi-one-dimensional bands.

Superconducting state breaks time-reversal symmetry with $oldsymbol{ extit{ extbf{p}}}_x + i oldsymbol{ extit{ extbf{p}}}_y$ symmetry.

The superconductor is topologically trivial, lacking robust edge modes.

Abstract

Using an asymptotically exact weak coupling analysis of a multi-orbital Hubbard model of the electronic structure of \SRO, we show that the interplay between spin and charge fluctuations leads unequivocally to triplet pairing which originates in the quasi-one dimensional bands. The resulting superconducting state spontaneously breaks time-reversal symmetry and is of the form $\Delta \sim p_x + i p_y \hat{z}$ with sharp gap minima and a d-vector that is only {\it weakly} pinned. The supercondutor is topologically {\it trivial} and hence lacks robust chiral Majorana fermion modes along the boundary. The absence of topologically protected edge modes could explain the surprising absence of experimentally detectable edge currents in this system.