Cuprate parameters from numerical Wannier functions

Abstract

We have developed a constrained-occupation local-density-functional technique to calculate individual model Hamiltonian parameters for states of arbitrary localization. The method generates numerical Wannier functions for the relevant states, and by decoupling these functions, permits direct calculation of the individual parameters. We have tested this method for the cuprate ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$, and obtained values for the Cu(3${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$) and O(2${\mathit{p}}_{\mathrm{\sigma }}$) parameters in general agreement with previous empirical and theoretical estimates. These calculations provide even-handed treatment of both Cu(3d) and the more extended O(2p) states, and yield the important difference ${\mathrm{\varepsilon }}_{\mathit{p}\left(\mathrm{\sigma }\right)}$-${\mathrm{\varepsilon }}_{\mathit{d}(\mathit{x}}^2$-${\mathit{y}}^2$) consistent with expectations based on the superexchange frequency. We also report parameter values for the Cu(3${\mathit{d}}_{3\mathit{z}}^2$-${\mathit{r}}^2$) states, and for compatible O(2p) states, which may be of use in theoretical attempts to confirm the symmetry of the doped-in carriers.