Heavy quasiparticles and Cooper-pair interaction in the Hubbard model

The Hubbard model is studied in the vicinity of the Mott transition. Local and quantal spin fluctuations are completely included through the mapping to the Anderson model; a local Kondo temperature $T_K$ is defined as their characteristic temperature or energy scale. Antiferromagnetic spin fluctuations are included perturbatively in terms of $\frac{1}{d}$ and to leading order in $\frac{k_B{T}_K}{U}$ with $d$ being the spatial dimensionality, $k_B$ the Boltzmann constant, and $U$ the intrasite repulsion. The two different kinds of spin fluctuations are responsible for the formation of heavy quasiparticles. Two intersite exchange interactions are responsible for both the development of the antiferromagnetic spin fluctuations and $d\gamma$-wave Cooper pairing between the heavy quasiparticles: the superexchange interaction and an exchange interaction due to the virtual exchange of spin excitations within the heavy quasiparticle band. An experimental specific-heat coefficient of about 14 mJ/${\mathrm{K}}^2$ Cu${\mathrm{O}}_2$ mol and a Wilson ratio of about 0.4 imply that the interplay between the local and the antiferromagnetic spin fluctuations plays a crucial role in both the normal and the superconducting states of $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ with critical temperatures of $T_c\simeq 90$ K. A pairing interaction deduced from the normal-state properties is strong enough to give critical temperatures as high as $T_{c0\mathrm{}}\simeq 200$ K in the absence of any pair breaking; there is experimental evidence that the pair-breaking effect of the antiferromagnetic spin fluctuations reduces $T_{c0\mathrm{}}\simeq 200$ K down to $T_{c0\mathrm{}}\simeq 90$ K.