Spin Gap and Superconductivity in Weakly Coupled Ladders: Interladder One-Particle vs. Two-Particle Crossover

Journal of the Physical Society of Japan (Impact Factor: 1.59). 09/1997; 66(12). DOI: 10.1143/JPSJ.66.3725
Source: arXiv


Effects of the interladder one-particle hopping, $t_{\perp}$, on the low-energy asymptotics of a weakly coupled Hubbard ladder system have been studied, based on the perturbative renormalization-group approach. We found that for finite intraladder Hubbard repulsion, $U$, there exists a crossover value of the interladder one-particle hopping, $t_{\perp c}$. For $0<t_{\perp}<t_{\perp c}$, the spin gap metal (SGM) phase of the isolated ladder transits at a finite transition temperature, $T_{c}$, to the d-wave superconducting (SCd) phase via a two-particle crossover. In the temperature region, $T<T_{c}$, interladder coherent Josephson tunneling of the Cooper pairs occurs, while the interladder coherent one-particle process is strongly suppressed. For $t_{\perp c}<t_{\perp}$, around a crossover temperature, $T_{cross}$, the system crosses over to the two-dimensional (2D) phase via a one-particle crossover. In the temperature region, $T<T_{cross}$, the interladdercoherent band motion occurs. Comment: 4 pages, 5 eps figures, uses jpsj.sty

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    ABSTRACT: Based on the perturbative renormalization group (PRG) approach, we have studied dimensional crossovers in Hubbard ladders coupled via weak interladder one-particle hopping, $t_{\perp}$. We found that the one-particle crossover is strongly suppressed through growth of the intraladder scattering processes which lead the isolated Hubbard ladder system toward the spin gap metal (SGM) phase. Consequently when $t_{\perp}$ sets in, there exists, for any finite intraladder Hubbard repulsion, $U>0$, the region where the two-particle crossover dominates the one-particle crossover and consequently the d-wave superconducting transition, which is regarded as a bipolaron condensation, occurs. By solving the scaling equations for the interladder one-particle and two-particle hopping amplitudes, we give phase diagrams of the system with respect to $U$, $t_{\perp0}$ (initial value of $t_{\perp}$) and the temperature, $T$. We compared the above dimensional crossovers with those in a weakly coupled chain system, clarifying the difference between them. Comment: 26 pages, 19 eps figures, to appear J. Phys. Soc. Jpn. Vol.67 No.5
    Full-text · Article · Feb 1998 · Journal of the Physical Society of Japan
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