Superconducting order of Sr2RuO4 from a three-dimensional microscopic model

Henrik S Røising,Steven H Simon,Felix Flicker,Thomas Scaffidi,Gunnar F Lange

doi:10.1103/physrevresearch.1.033108

Henrik S Røising, Steven H Simon + Show 3 more

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https://doi.org/10.1103/physrevresearch.1.033108

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Abstract

We compute and compare even- and odd-parity superconducting order parameters of strontium ruthenate ($\mathrm{Sr}_2\mathrm{RuO}_4$) in the limit of weak interactions, resulting from a fully microscopic three-dimensional model including spin-orbit coupling. We find that odd-parity helical and even-parity $d$-wave order are favored for smaller and larger values of the Hund's coupling parameter $J$, respectively. Both orders are found compatible with specific heat data and the recently-reported nuclear magnetic resonance (NMR) Knight shift drop [A. Pustogow et al. Nature 574, 72 (2019)]. The chiral $p$-wave order, numerically very competitive with helical order, sharply conflicts with the NMR experiment.

Highlights

Superconductivity was discovered in the layered perovskite strontium ruthenate, Sr2RuO4 (SRO), about 25 years ago [1]
As a function of the ratio of the Hund’s coupling J to the Hubbard interaction strength U we find a transition at J/U ≈ 0.15 from an odd-parity helical phase with accidentalnodes to an even-parity phase with symmetry-imposed vertical line nodes, both of which are compatible with several key experiments, but are not compatible with the observation of time-reversal symmetry breaking (TRSB)
The low-temperature values of Kx arguably appear in best agreement with d-wave order. It would be desirable, perhaps technically difficult, to have. Both the d-wave and helical orders found in this calculation have verticalnodes, and seem compatible with specific heat data and recent Knight shift measurements [20]

Summary

Introduction

Superconductivity was discovered in the layered perovskite strontium ruthenate, Sr2RuO4 (SRO), about 25 years ago [1]. A very recent in-plane field NMR experiment measured a significant spin susceptibility drop [20], contradicting the original measurements, which in the absence of spin-orbit coupling (SOC) would exclude all models featuring vectorial order parameters (triplet) pointing out of the basal plane [21]. This has reignited a longstanding debate, possibly making the case of helical or even-parity order parameters plausible [19,22,23,24]. That strong SOC [25,26,27] in a multi-orbital system complicates the analysis of the magnetic susceptibility compared to the single orbital case [9]

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