Theory of high-Tcsuperconductors within an Anderson lattice model

An Anderson lattice model for high-$T_c$ superconductors, in particular ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$, is set up and explicitly transformed into a slave-boson representation. The model is solved using a formal $\frac{1}{N}$ expansion technique, where $N$ is the degeneracy of the $d^9$ state, working to leading-$N$ approximation in the normal state and $\mathrm{O}\left(\frac{1}{N}\right)$ in the superconducting state. Normal-state properties such as susceptibility, density of states, and the location of added holes are calculated and compared with experiment. The model is an $s$-wave superconductor in the present approximation for realistic parameters. The gap-to-$T_c$ ratio, specific-heat jump, and $H_c\mathrm{}\left(0\right)\mathrm{}$ take their Bardeen-Cooper-Schrieffer values. The variation of $T_c$ with doping is successfully explained. A calculation of the critical region, taking into account strong tetragonal anisotropy, finds its width of order 1 K, in agreement with experiment.