Strong magnetic field enhancement of spin triplet pairing arising from coexisting $2k_F$ spin and $2k_F$ charge fluctuations

We study the effect of the magnetic field (Zeeman splitting) on spin triplet superconductivity. We show generally that the enhancement of spin triplet pairing mediated by coexisting $2k_F$ spin and $2k_F$ charge fluctuations can be much larger than in the case of triplet pairing mediated by ferromagnetic spin fluctuations. We propose that this may be related to the recent experiment on ${\left(\text{TMTSF}\right)}_2{\text{ClO}}_4$, in which the possibility of a singlet to triplet pairing transition has been suggested.

Figure 1

Diagrammatic view for the presence of (a) only the on-site repulsion and (b) the off-site repulsions in $U+V\left({\mathbf{Q}}_{2k_F}\right)=0$.

Figure 2

(Color online) (a) The model on the triangular lattice (left), the $f$-wave gap (center), and the DOS in the presence of Zeeman splitting (right). The Fermi level is for a dilute band filling. (b) The Q1D model for ${\left(\text{TMTSF}\right)}_{2}X$ (left), and $d$-wave (center) and $f$-wave (right) gaps along with the Fermi surface. The arrows represent the nesting vector.

Figure 3

(Color online) ${\alpha }_{\sigma }\left(\mathbf{q},B\right)$ at $T=0.02$ for (a) the triangular lattice with $n=0.2$ and (b) the Q1D model with $V_2+V_y=0.85=U/2$.

Figure 4

(Color online) $B$ dependence of $\lambda$ at $T=0.02$ for (a) the triangular lattice with $n=0.2$ and (b) the Q1D model with $V_2+V_y=U/2$. (c) $B$ dependence of the most dominant $\lambda$ for the cases shown in (a) and (b) normalized by $\lambda$ at $B=0$. (d) $B$ dependence of $\lambda$ in the Q1D model for $V_2+V_y=0.8<U/2$ at $T=0.012$.

Figure 5

(Color online) (a) Pairing “phase diagram” obtained by comparing $\lambda$ at $k_{B}T=0.012$. (b) Calculated $T\text{−}B$ phase diagram in $V_2=0.4$ and $V_y=0.4$. $T_c$ is determined by the condition $\lambda =1$, and the boundary (dashed line) between $d$ and $f$ should be considered as just a guideline.