Spin gap and superconductivity in weakly coupled ladders: Interladder one-particle vs. two-particle crossover

Effects of the interladder one-particle hopping, t(perpendicular to), 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(perpendicular to c). For 0 < t(perpendicular to) < t(perpendicular to 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 tie < tl, 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 interladder coherent band motion occurs.