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.
Categories: cond-mat.supr-con cond-mat.str-el