APW-LCAO band model forA15compounds

Abstract

The results of nonrelativistic augmented-plane-wave (APW) band-structure calculations at symmetry points in the cubic Brillouin zone for ${\mathrm{V}}_3$Si, ${\mathrm{V}}_3$Ge, ${\mathrm{Nb}}_3$Al, and ${\mathrm{Nb}}_3$Sn are fit using the Slater-Koster linear-combination-of-atomic-orbitals (LCAO) interpolation scheme. This LCAO model involves Bloch sums formed from 30 $A$-atom ($A=\mathrm{V},\mathrm{N}\mathrm{b}$) $d$ orbitals and eight $B$-atom ($B=\mathrm{S}\mathrm{i},\mathrm{G}\mathrm{e},\mathrm{A}\mathrm{l},\mathrm{S}\mathrm{n}$) $s-p$ orbitals. In its simplest form, this LCAO model fits 73 APW energy eigenvalues at $\Gamma$, $X$, $M$, and $R$ with an rms error of 0.020-0.023 Ry by means of 21 two-center parameters. Improved accuracy is achieved, particularly for states near $E_F$, by weighting these more heavily in the LCAO fit, partially relaxing the two-center approximation, and increasing the number of LCAO parameters to 39. The results of this APW-LCAO model are applied to evaluate the accuracy of the Labbé-Friedel (LF) linear-chain and the Weger-Goldberg (WG) coupled-chain band models for the $A15$ compounds. It is concluded that (a) corrections to the LF and WG models (about 3 and 1 eV, respectively) are sufficient to wash out fine structure in the density of states on a meV energy scale; (b) there is no evidence for describing the electronic structure of these $A15$ as one-dimensional or quasi-one-dimensional in character; (c) the density-of-states peak near $E_F$ involves primarily $A$-atom $d$ states with ${\delta }_1(x^2-y^2)$ symmetry, in contrast to the predictions of the $\mathrm{LF} ({\delta }_1+{\delta }_2)$ and $\mathrm{WG} \left({\delta }_2\right)$ models; (d) the accuracy of the present LCAO model is insufficient for predicting the precise shape of the density of states near $E_F$ from first principles.