Anisotropic Superconductivity Emerging from the Orbital Degrees of Freedom in a $\Gamma_3$ Non-Kramers Doublet System

Abstract

We study superconductivity in a three-orbital model for $f^2$ ions with the $\Gamma_3$ crystalline electric field (CEF) ground state. An antiferromagnetic interaction between the $\Gamma_7$ and $\Gamma_8$ orbitals is introduced to stabilize the $\Gamma_3$ CEF state. This interaction also works as an on-site attractive interaction for spin-singlet pairing between electrons in these orbitals. The interorbital pairing state composed of the $\Gamma_7$ and $\Gamma_8$ orbitals on the same site has the $E_g$ symmetry. Indeed, by applying the random phase approximation, we find that the $E_g$ spin-singlet superconducting state is realized over a wide parameter range.