Cluster Studies of La₂CuO₄ Geometric Distortions Accompanying Doping

Conclusions

First principles cluster calculations, such as those discussed here, can and have been used to address some issues important in high-temperature superconductivity. In these studies, one grapples with the usual problems governing accuracy in small molecules: the completeness of the one- and many-electron basis sets. In addition, the appropriateness of the background potential and the convergence of the results as a function of cluster size must be concerns as well. Certain questions, such as the magnitude of the spin exchange constant, the positions of the crystal-field excitations, and the interpretation of the photoemission spectrum, can be addressed semi-quantitatively with first principles quantum chemistry methods applied to quite small clusters. Other properties (e.g. transport, pairing susceptibilities, etc.) require a more extended lattice, and therefore attempts to generate parameters for models which can be extended to larger clusters have also been the focus of SCF/CI and DFT studies. This bootstrap approach is pragmatic, but unsettling. There is always the worry that in mapping the results onto a simpler model, one throws out the baby with the bathwater. In the current context, I have discussed the origin and magnitude of an on-site electron-phonon coupling in single-band models of the cuprates. The correlations responsible for the broken-symmetry “electronic polaron” solutions are, however, not explicitly included in a single-band model; they require retention of both the O2p and Cu3d degrees of freedom. Are these important for the mechanism of superconductivity, or is it permissible to think of them as simply renormalizing the effective parameters of a single-band model? It is clear that there are many such unanswered questions in this field, and I believe cluster calculations will continue to contribute to their solution.