Pairing competition in a quasi-one-dimensional model of organic superconductors (TMTSF)$_{2}X$ in magnetic field

TL;DR

This paper explores how magnetic fields influence superconducting states in quasi-one-dimensional organic materials, revealing complex phase transitions and mixing of pairing states due to charge and spin fluctuations.

Contribution

It provides a detailed phase diagram showing transitions between singlet, FFLO, and triplet pairings under magnetic fields, incorporating charge fluctuation effects.

Findings

Consecutive transitions from singlet to FFLO and triplet states with increasing magnetic field.

Strong mixing of singlet d-wave and triplet f-wave components in the FFLO state.

Charge fluctuations significantly influence the pairing competition and phase transitions.

Abstract

We microscopically study the effect of the magnetic field (Zeeman splitting) on the superconducting state in a model for quasi-one-dimensional organic superconductors (TMTSF)$_{2}X$. We investigate the competition between spin singlet and spin triplet pairings and the Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) state by random phase approximation. While we studied the competition by comparison with the eigenvalue of the gap equation at a fixed temperature in our previous study (Phys. Rev. Lett. \textbf{102} (2009) 016403), here we obtain both the $T_c$ for each pairing state and a phase diagram in the $T$(temperature)-$h_z$(field)-$V_y$(strength of the charge fluctuation) space. The phase diagram shows that consecutive transitions from singlet pairing to the FFLO state and further to $S_z=1$ triplet pairing can occur upon increasing the magnetic field when $2k_{F}$ charge fluctuations coexist with $2k_{F}$ spin fluctuations. In the FFLO state, the singlet d-wave and $S_{z}=0$ triplet $f$-wave components are strongly mixed especially when the charge fluctuations are strong.