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The search for realistic one-dimensional (1D) models that exhibit dominantsuperconducting (SC) fluctuations effects has a long history. In these 1Dsystems, the effects of commensurate band fillings--strongest athalf-filling--and electronic repulsions typically lead to a finite charge gapand the favoring of insulating density wave ordering over superconductivity.Accordingly, recent proposals suggesting a gapless metallic state in theHolstein-Hubbard (HH) model, possibly superconducting, have generatedconsiderable interest and controversy, with the most recent work demonstratingthat the putative dominant superconducting state likely does not exist. In thispaper we study a model with non-local electron-phonon interactions, in additionto electron-electron interactions, this model unambiguously possesses dominantsuperconducting fluctuations at half filling in a large region of parameterspace. Using both the numerical multi-scale functional renormalization groupfor the full model and an analytic conventional renormalization group for abosonized version of the model, we demonstrate the existence of dominantsuperconducting (SC) fluctuations. These dominant SC fluctuations arise becausethe spin-charge coupling at high energy is weakened by the non-localelectron-phonon interaction and the charge gap is destroyed by the resultantsuppression of the Umklapp process. The existence of the dominant SC pairinginstability in this half-filled 1D system suggests that non-localboson-mediated interactions may be important in the superconductivity observedin the organic superconductors.

Dominant Superconducting Fluctuations in the One-Dimensional Extended Holstein-Extended Hubbard model