Theory of Fulde-Ferrell-Larkin-Ovchinnikov state of superconductors with and without inversion symmetry: Hubbard model approach

TL;DR

This paper investigates the FFLO superconducting state in systems with and without inversion symmetry using the Hubbard model, revealing how symmetry influences the momentum of Cooper pairs and the emergence of specific pairing states.

Contribution

It provides a theoretical analysis of the FFLO state considering inversion symmetry and spin-orbit coupling, highlighting the favored pairing symmetries and the effects of magnetic field and RSOC.

Findings

Center of mass momentum Q aligns with axes with inversion symmetry

Q is perpendicular to magnetic field without inversion symmetry

Favored pairing is d+f-wave, with a triplet f-wave component present

Abstract

We study Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of superconductors with and without inversion symmetry based on the Hubbard model on the square lattice near half-filling, using the random phase approximation. We show that center of mass momentum $Q$ tends to be parallel to $x$- or y-axis in the presence of inversion symmetry, while $Q$ vector is likely to be perpendicular to the magnetic field in the absence of inversion symmetry. We also clarify that $d+f$-wave pairing is favored and the hetero spin triplet $f$-wave state is present in the FFLO state unlike state in the superconductors only with the Rashba type spin-orbit coupling (RSOC) originating from the broken inversion symmetry. The triplet $f$-wave state is enhanced by magnetic field and the RSOC. This stems from the reduction of the spin susceptibilities by the magnetic field and the RSOC.