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arXiv:cond-mat/9403024 · Physical review. B, Condensed matter

Superconducting fluctuations in one-dimensional multiband models

M. I. Salkola, Alexander V. Balatsky

Published Jun 1, 1995• 0 citations
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Abstract

A renormalization-group and bosonization approach for a multiband Hamiltonian in one dimension is described. Based on the limit of many bands, it is argued that this Hamiltonian with bare repulsive electron-electron interactions is scaled under specific conditions to a model in which superconducting ordering fluctuations dominate.
DOI
10.1103/physrevb.51.15267

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The search for realistic one-dimensional (1D) models that exhibit dominant superconducting (SC) fluctuations effects has a long history. In these 1D systems, the effects of commensurate band fillings---strongest at half-filling---and electronic repulsions typically lead to a finite charge gap and the favoring of insulating density wave ordering over superconductivity. Accordingly, recent proposals suggesting a gapless metallic state in the Holstein-Hubbard (HH) model, possibly superconducting, have generated considerable interest and controversy, with the most recent work demonstrating that the putative dominant superconducting state likely does not exist. In this paper we study a model with nonlocal electron-phonon interactions, in addition to electron-electron interactions. This model unambiguously possesses dominant superconducting fluctuations at half filling in a large region of parameter space. Using both the numerical multi-scale functional renormalization group (MFRG) for the full model and an analytic conventional renormalization group for a bosonized version of the model, we demonstrate the existence of these dominant SC fluctuations and show that they arise because the spin-charge coupling at high energies is weakened by the nonlocal electron-phonon interaction and the charge gap is destroyed by the resultant suppression of the Umklapp process. The existence of the dominant SC pairing instability in this half-filled 1D system suggests that nonlocal boson-mediated interactions may be important in the superconductivity observed in the organic superconductors.
We consider a one-dimensional model of interacting electrons. The Fermi surface crosses two bands, with light and heavy masses, respectively. Both intraband and interband interactions are assumed. The earlier renormalization-group treatment of the model by Varma and Zawadowski is extended to check the validity of the scaling assumption and to calculate the next corrections to the scaling equations. These corrections indicate a Fermi-velocity renormalization. Depending on the initial parameters, two kinds of behavior can appear. Either the interband charge fluctuations are negligible and then the dominant instabilities are determined by the interband exchange and the intraband backscattering with the two velocities remaining different, or the interband charge fluctuations become dominant and the velocities scale to a common value. The phase diagram of the model is also determined.
A multiband Hubbard Hamiltonian (close to the one used to describe CuO2{\mathrm{CuO}}_{2}CuO2​ planes) is studied with strong-coupling perturbation theory. Two charge-fluctuation mechanisms are described and lead to a spin-independent attraction, which is much larger than the antiferromagnetic interaction. It provides a convincing argument for the possibility of superconductivity induced by repulsive interactions.
A two-band model of spinless fermions in one dimension is constructed. Density-density couplings, umklapp scattering, and interband transitions are included. Renormalization-group equations are derived and discussed. In addition, it is shown that with one condition on the couplings and the velocities the model may be transformed to two uncoupled sine-Gordon Hamiltonians, which makes it possible to obtain solutions in regions where the renormalization-group equations are not valid. An important property of the model is that there can be superconductivity with repulsive interactions.