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Physical review. B, Condensed matter

Superconducting instability study in a one-dimensional repulsive system with a doubly degenerate band

Sujit Sarkar

Published Aug 20, 2001• 0 citations
Publisher

Abstract

Superconducting instability is studied for a one dimensional repulsive system of spinful fermions with double degenerate band. There is no evidence of insulating spin liquid or the D-Mott phase, for any generic fillings. A conventional spin gap phase without any gap in the charge sector (metallic spin gap) is predicted, which is the starting point to investigate the gapless superconducting instability.

DOI
10.1103/physrevb.64.104407

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Superconducting instability is studied for a one dimensional repulsive system of spinful fermions with double degenerate band. There is no evidence of insulating spin liquid or the D-Mott phase, for any generic fillings. A conventional spin gap phase without any gap in the charge sector (metallic spin gap) is predicted, which is the starting point to investigate the gapless superconducting instability.
The zero-temperature phase diagram of a ppp-orbital two-component fermionic system loaded into a one-dimensional optical lattice is mapped out by means of analytical and numerical techniques. It is shown that the ppp-band model away from half-filling hosts various competing superconducting phases for attractive and repulsive interactions. At quarter-filling, we analyze the possible formation of incompressible Mott phases and in particular for repulsive interactions, we find the occurrence of a Mott transition with the formation of fully gapped bond-ordering waves.
We study the phase diagram of a one-dimensional Hubbard model where, in addition to the standard nearest-neighbor hopping t, we also include a next-to-nearest-neighbor hopping ${\mathit{t}}^{\ensuremath{'}}$. For strong enough on-site repulsion, this model has a transition at half filling from a magnetic insulator with gapless spin excitations at small ${\mathit{t}}^{\ensuremath{'}}$/t to a dimerized insulator with a spin gap at larger ${\mathit{t}}^{\ensuremath{'}}$/t. We show that upon doping this model exhibits quite interesting features, which include the presence of a metallic phase with a spin gap and dominant superconducting fluctuations, in spite of the repulsive interaction. More interestingly, we find that this superconducting phase can be reached upon hole doping the magnetic insulator. The connections between this model and the two chain models, recently object of intensive investigations, are also discussed. \textcopyright{} 1996 The American Physical Society.
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 the multiband, purely repulsive Hubbard model on a class of systems in which there are two (or more) kinds of orbitals per unit cell such that one metallic band interacts with the other insulating band. From both perturbational canonical transformation and quantum Monte Carlo studies we have shown that superconductivity due to nonretarded attraction (negative U) is a generic feature of this class of metal-insulator composite many-body systems. Remarkably, the superconductivity arises, under appropriate conditions, for various types of insulating bands (a charge-transfer insulator, Mott-Hubbard insulator, etc.). Superconductivity is unambiguously identified from the pairing correlation function, which agrees with that of the attractive Hubbard model surprisingly well even in the nonperturbative regime. The superconductivity revealed here is in a sense an opposite limit to conventional superconductivity with retarded attraction from boson-exchange mechanisms. We also show that the present mechanism is distinct from existing multiband models such as d-${\mathit{p}}_{\mathrm{\ensuremath{\sigma}}}$ models. As we increase the magnitude of the attraction in the present model by changing some parameters (e.g., to make the accompanying band metallic), the similarity with the attractive Hubbard model becomes eventually degraded, so that the optimum condition for superconductivity is determined by this kind of tradeoff. We also discuss the relevance of the present model to high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductivity in cuprates and fullerenes.
We have obtained the quantum phase diagram of one dimensional extended Bose-Hubbard model using the density-matrix renormalization group and Abelian bosonization methods for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from Mott insulating phase to superconducting phase for integer band fillings of bosons. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, apart from the charge density wave and superconducting phases for half-integer band fillings. Our study reveals that extended range interactions are necessary to get the correct phase boundary of an one-dimensional interacting bosons system.
The phase diagram of one-dimensional alkaline-earth fermionic atoms and ytterbium 171 atoms is investigated by means of a low-energy approach and density-matrix renormalization group calculations. For incommensurate filling, four gapless phases with a spin gap are found and consist of two superconducting instabilities and two coexisting bond and charge density-waves instabilities. In the half-filled case, seven Mott-insulating phases arise with the emergence of four non-degenerate phases with exotic hidden orderings.