Temperature and doping dependence of the singlet and triplet pair susceptibilities in the one-band Hubbard model based on the dynamical mean-field theory

We investigate the superconductivity in the one-band Hubbard model on the basis of the dynamical mean-field theory (DMFT) [1], in which the irreducible vertex function $\Gamma$ has no k-dependence and then only the s-wave superconductivities with the spin-singlet even-frequency pairing and the spin-triplet odd-frequency pairing are possibly realized. In the previous DMFT studies, both the singlet and triplet superconductivities have not been observed in the one-band Hubbard model [2,3] in contrast to the case with the two-band Hubbard model where the singlet and/or triplet superconductivities are found to be realized [3,4,5]. However, the detailed results of the pair (superconducting) susceptibilities over the whole parameter regime including quite low temperatures where the superconductivity is expected to be realized were not been explicitly shown there [2,3]. Then, we calculate the singlet and triplet pair susceptibilities in the one-band Hubbard model for a wide range of parameters: the electron number per site n, the temperature T and the on-site Coulomb interaction U. The singlet (triplet) pair susceptibility is constructed by ladder diagrams of the particle-particle channel with respect to the singlet (triplet) irreducible vertex function $\Gamma _{s}$ ($\Gamma_{t}$) which corresponds to an effective interaction leading singlet (triplet) pairing and is obtained by solving the Bethe-Salpeter equation with the use of the linearized DMFT [6] developed for describing the electronic state close to the Mott transition. In the explicit calculations, we use the Bethe lattice with the band width of 4eV where the Mott transition takes place at Uc=6eV for n=1 within the linearized DMFT. We obtain the T dependence of the singlet and triplet pair susceptibilities $\chi_{s}$ and $\chi_{t}$ for several values of n and U, respectively. We find that $\chi_{s}$ is suppressed by the repulsion U especially for the region near the Mott transition as consistent with the previous studies [2,3], while $\chi_{t}$ is apparently enhanced by U at very low temperature below 10K where the effective interaction for the triplet pairing is considered to be attractive and then the triplet superconductivity is expected to be realized at further low temperatures below 1K.

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