Influence of spin fluctuations on the superconducting transition temperature and resistivity in the t-J model at large N - art. no. 064520

Spin fluctuations enter the calculation of the superconducting transition t emperature T-c only in the next-to-leading order [i.e., in O(1/N-2)] of the 1/N expansion of the t-J model. We have calculated these terms and show th at they have only little influence on the value for T-c obtained in the lea ding order O(1/N) in the optimal and overdoped region, i.e., for dopings la rger than the instability towards a flux phase. This result disagrees with recent spin-fluctuation mediated pairing theories. The discrepancies can be traced back to the fact that in our case the coupling between electrons an d spins is determined by the t-J model and not adjusted and that the spin s usceptibility is rather broad and structureless and not strongly peaked at low energies as in spin-fluctuation models. Relating T-c and transport we s how that the effective interactions in the particle-particle and particle-h ole channels are not simply related within the 1/N expansion by different F ermi surface averages of the same interaction as in the case of phonons or spin fluctuations. As a result, we find that large values for T-c and rathe r small scattering rates in the normal state as found in the experiments ca n easily be reconciled with each other. We also show that correlation effec ts heavily suppress transport relaxation rates relative to quasiparticle re laxation rates in the case of phonons but not in the case of spin fluctuati ons.