Spin-triplet superconductivity in Sr2RuO4 due to orbital and spin fluctuations: Analyses by two-dimensional renormalization group theory and self-consistent vertex-correction method

TL;DR

This paper demonstrates that orbital and spin fluctuations, enhanced by vertex corrections, mediate triplet superconductivity in Sr2RuO4, confirmed by two advanced theoretical methods, revealing a specific gap structure influenced by spin-orbit interaction.

Contribution

It introduces a combined RG+cRPA and self-consistent vertex correction approach to confirm orbital and spin fluctuations as the mechanism for triplet superconductivity in Sr2RuO4.

Findings

Orbital and spin fluctuations at Q ≈ (2π/3, 2π/3) are crucial.

Triplet pairing in the Eu representation with sin 3k_x and sin 3k_y gap functions.

Large superconducting gap on the d_xy orbital FS induced by quasi-1D FS gaps.

Abstract

We study the mechanism of the triplet superconductivity (TSC) in Sr$_2$RuO$_4$ based on the multiorbital Hubbard model. The electronic states are studied using the recently developed renormalization group method combined with the constrained random-phase-approximation, called the RG+cRPA method. Thanks to the vertex correction (VC) for the susceptibility, which is dropped in the mean-field-level approximations, strong orbital and spin fluctuations at $Q \approx(2\pi/3,2\pi/3)$ emerge in the quasi one-dimensional Fermi surfaces (FSs) composed of $d_{xz}+d_{yz}$ orbitals. Due to the cooperation of both fluctuations, we obtain the triplet superconductivity in the $E_u$ representation, in which the superconducting gap is given by the linear combination of $(\Delta_x(k),\Delta_y(k))\sim (\sin 3k_x,\sin 3k_y)$. Very similar results are obtained by applying the diagrammatic calculation called the self-consistent VC method. Thus, the idea of "orbital+spin fluctuation mediated TSC" is confirmed by both RG+cRPA method and the self-consistent VC method. We also reveal that a substantial superconducting gap on the $d_{xy}$-orbital FS is induced from the gaps on the quasi one-dimensional FSs, in consequence of the large orbital-mixture due to the 4$d$ spin-orbit interaction.