Orbitally selective breakdown of the Fermi liquid and simultaneous enhancement of metallic and insulating states in correlated multiband systems with spin-orbit coupling

Abstract

We show that spin-orbit coupling (SOC) plays Janus-faced roles on the orbitally-selective Mott transitions in a three-orbital Hubbard model with crystal field splitting at a specific filling of 2/3, which is a minimal Hamiltonian for ruthenates. While the SOC favors metallic state due to enhancement of orbital hybridization at smaller on-site Coulomb repulsions, it stabilizes the Mott insulating state ascribed to lifting of orbital degeneracies and enhancement of band polarizations at larger electronic interaction. Moreover, an orbitally-selective non-Fermi liquid (OSnFL), where breakdown and retention of the Fermi liquid coexist in different orbitals, emerges between the orbitally-selective Mott phase and the Fermi-liquid state. This novel state can be used to account for the exotic metallic behavior observed in 4d materials, such as Ca1.8Sr0.2RuO4, Ba2RuO4 under strain and Sr2RuO4 under uniaxial pressure. We propose that orbitally-selective Kondo breakdown may account for the OSnFL.