Strong Parity Mixing in the Fulde-Ferrell-Larkin-Ovchinnikov Superconductivity in Systems with Coexisting Spin and Charge Fluctuations

We study the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of spin fluctuation mediated pairing, and focus on the effect of coexisting charge fluctuations. We find that (i) consecutive transitions from singlet pairing to FFLO and further to $S_z=1$ triplet pairing can generally take place upon increasing the magnetic field when strong charge fluctuations coexist with spin fluctuations, and (ii) the enhancement of the charge fluctuations lead to a significant increase of the parity mixing in the FFLO state, where the triplet/singlet component ratio in the gap function can be close to unity. We propose that such consecutive pairing state transition and strong parity mixing in the FFLO state may take place in a quasi-one-dimensional organic superconductor $(\mathrm{TMTSF}{)}_{2}X$.

Figure 1

(a) The model adopted in this study. (b) Schematic figure of the gap for $d$ wave (left) and $f$ wave (right), where the blue dashed lines are the nodes of the gap, and the red solid curves are the disconnected Fermi surface.

Figure 2

Upper panels: the $h_z$ dependence of $Q_{cx}$ (right axis) and the $S_z=0$ triplet/singlet ratio ${\varphi }_{\mathrm{ST}{f}^0}/{\varphi }_{\mathrm{SS}d}$ (left axis) in the FFLO. Lower panels: the eigenvalues of the gap equation. (a) $V_x=0$ and (b) $V_x=0.65$. Other parameters are $U=1.5$, $n=1.1$, $t_y=0.5$, $V_{x2}=V_{x3}=V_y=0$, and $T=0.01$.

Figure 3

The $V_x$ dependence of (a) the ratio ${\varphi }_{\mathrm{ST}{f}^0}/{\varphi }_{\mathrm{SS}d}$ and (b) the ratio of the eigenvalues between the $S_z=0$ triplet and the singlet pairings. Other parameters are the same with Fig. 2.

Figure 4

Upper panels: the $h_z$ dependence of $Q_{cx}$ (right axis) and the triplet/singlet ratio ${\varphi }_{\mathrm{ST}{f}^0}/{\varphi }_{\mathrm{SS}d}$ (left). Lower panels: the eigenvalues of the gap equation. (a) $V_y=0$ and (b) $V_y=0.35$. Other parameters are $U=1.7$, $V_x=0.9$, $V_{x2}=0.45$, $V_{x3}=0.1$, $t_y=0.2$, $n=1.5$, and $T=0.012$.

Figure 5

A pairing phase diagram in $V_y\mathrm{\text{−}}{h}_z$ space, where the green circles represent the singlet $d$ wave, the red squares the FFLO, the blue triangles the $S_z=1$ triplet $f$ wave, and the filled diamonds in the hatched area $\mathrm{SDW}+\mathrm{CDW}$ instability. The eigenvalue is represented by the contours and also by the size of the symbols.