Electronic orders in multi-orbital Hubbard models with lifted orbital degeneracy

TL;DR

This paper investigates symmetry-broken phases in multi-orbital Hubbard models with lifted orbital degeneracy, revealing new spin-orbital orders and effects of crystal field splitting on superconductivity using dynamical mean field theory.

Contribution

It introduces a method to measure four-point correlation functions for lattice susceptibilities and explores the impact of crystal field splitting on superconducting states in multi-orbital models.

Findings

Metallic phase becomes unstable to spin-orbital order without spin or orbital moments.

Higher energy orbitals can dominate superconductivity, enhancing T_c.

Crystal field splitting influences the relevance of orbitals for superconductivity.

Abstract

We study the symmetry-broken phases in two- and three-orbital Hubbard models with lifted orbital degeneracy using dynamical mean field theory. On the technical level, we explain how symmetry relations can be exploited to measure the four-point correlation functions needed for the calculation of the lattice susceptibilities. In the half-filled two-orbital model with crystal field splitting, we find an instability of the metallic phase to spin-orbital order with neither spin nor orbital moment. This ordered phase is shown to be related to the recently discovered fluctuating-moment induced spin-triplet superconducting state in the orbitally degenerate model with shifted chemical potential. In the three-orbital case, we consider the effect of a crystal field splitting on the spin-triplet superconducting state in the model with positive Hund coupling, and the spin-singlet superconducting state in the case of negative Hund coupling. It is demonstrated that for certain crystal field splittings the higher energy orbitals instead of the lower ones are relevant for superconductivity, and that $T_c$ can be enhanced by the crystal field effect. We comment on the implications of our results for the superconductivity in strontium ruthenates, and for the recently reported light-enhanced superconducting state in alkali-doped fullerides.