Weak coupling approach to magnetic and orbital susceptibilities for superconducting states in multiorbital electron-phonon coupled model

TL;DR

This paper investigates the magnetic and orbital susceptibilities in multiorbital superconductors, revealing that electric orbital fields influence the superconducting state while magnetic fields do not, using Eliashberg theory with Jahn-Teller phonons.

Contribution

It introduces a weak coupling approach to analyze magnetic and orbital susceptibilities in multiorbital electron-phonon coupled models, emphasizing the role of electric orbital fields.

Findings

Magnetic Zeeman field is inactive for singlet pairing.

Magnetic orbital field is inactive in the superconducting state.

Electric orbital field remains active and influences the superconducting phase.

Abstract

Alkali-doped fullerides are molecular-based superconductors with multiple active orbitals. In this paper, using the Eliashberg theory with the retardation effect of Jahn-Teller phonons, we study the response of the spin-singlet superconducting state relevant to fulleride materials. The spin Zeeman field is not active for the singlet pairing state, and the magnetic orbital field, which physically generates a circular electron motion inside the fullerene molecule, is also shown to be inactive. On the other hand, the electric orbital (or quadrupolar) field, which corresponds to a uniaxial distortion, remains active across the superconducting phase transition. This is understood by the orbital-symmetric structure of the Cooper pair, which is susceptible to the electric orbital field, while it is not the case for the magnetic orbital field which tends to create an antisymmetric part.