Competition of pairing symmetries and a mechanism for Berezinskii pairing in quasi-one-dimensional systems

We revisit the pairing symmetry competition in quasi-one-dimensional systems. We show that spin-triplet $s$-wave pairing, where the pair is formed by electrons with different times and has an odd-frequency symmetry, can be realized in systems with one-dimensionality when the strength of charge fluctuation exceeds that of spin fluctuation. The present study provides a mechanism for this exotic pairing proposed by Berezinskii [JETP Lett. 20, 287 (1974)].

Figure 1

Pictures of the momentum $\mathit{k}=(k_x,k_y)$ dependences of $\Delta$. Upper panels show sign change (positive or negative) of $\Delta$ with nodes (black dashed lines) in momentum space. (Purple) solid curves denote the Fermi surface with the nesting vectors (arrows). Lower panels show the $k_x$ dependences of $\Delta$. (A) $d$ wave in SF $>$ CF case with moderate two-dimensionality. (B) $f$ wave in CF $>$ SF case with moderate two-dimensionality. (C) $p$ wave in SF $>$ CF case with weak two-dimensionality. (D) $s$ wave in CF $>$ SF case with weak two-dimensionality.

Figure 2

The model considered in the present study. $t_x$, $t_y$, and $t_d$ are the hopping integrals. $U$ and $V$ are the on-site and off-site Coulomb repulsions, respectively.

Figure 3

$T$ dependences of $\lambda$ for SF $>$ CF or CF $>$ SF and for moderate or weak two-dimensionality. Insets (k) and ($\mathrm{\omega }$) are $k_x$ and ${\omega }_n$ dependences of $\Delta$ corresponding to the largest $\lambda$, respectively. In the inset (k), we choose $k_y=0$ and ${\omega }_n=\pi T$. $k_{\mathrm{F}}$ in the inset denotes the location of the Fermi surface at $k_y=0$. In the inset ($\mathrm{\omega }$), we choose $\mathit{k}$ where $\Delta$ gets the largest value on $k_y=0$.

Figure 4

The most stable pairings dependent on the strength of one-dimensionality and spin/charge fluctuation.