Microscopic Identification of the D-vector in Triplet Superconductor Sr_2RuO_4

TL;DR

This paper microscopically investigates the internal degrees of freedom of triplet superconductivity in Sr_2RuO_4, revealing how the chiral p-wave state is stabilized through orbital-dependent interactions influenced by Hund coupling and spin-orbit effects.

Contribution

It demonstrates that the chiral p-wave state in Sr_2RuO_4 is stabilized by a combination of Hund coupling and spin-orbit interaction within a three-band Hubbard model.

Findings

Chiral p-wave state stabilized in the bb-band

Orbital-dependent superconductivity is robust in Sr_2RuO_4

Hund coupling and spin-orbit interaction are essential for symmetry breaking

Abstract

Triplet superconductivity in Sr_2RuO_4 is investigated with main interest on its internal degree of freedom. We perform a microscopic calculation to investigate how the chiral state d(k) = (k_x \pm ik_y)z is realized among the underlying six degenerate states. Starting from the three band Hubbard model with spin-orbit interaction, we use a perturbation theory in order to calculate the pairing interaction. The p-wave superconductivity with T_c \sim 1.5K is obtained in the moderately weak coupling region. It is shown that the orbital dependent superconductivity (ODS) robustly appears in Sr_2RuO_4. We determine the stabilized state by solving the Eliashberg equations. It is found that the Hund coupling term as well as the spin-orbit interaction is necessary for the ``symmetry breaking interaction''. The main result is that the chiral state is stabilized in case of the p-wave symmetry with the main \gamma-band, which is obtained in the perturbation theory. When we assume the other pairing symmetry including the f-wave state, the symmetry breaking interaction gives the other D-vector. The electronic structure constructed from the t_2g-orbitals is essential for this result.