Self-consistent augmented-plane-wave electronic-structure calculations for theA15compoundsV3XandNb3X,X=Al,Ga,Si,Ge,andSn

We have performed self-consistent (SC) band-structure calculations for the $A15\mathrm{}$ compounds ${\mathrm{V}}_{3}X$ and ${\mathrm{Nb}}_{3}X$, $X=\mathrm{A}\mathrm{l},\mathrm{G}\mathrm{a},\mathrm{S}\mathrm{i},\mathrm{G}\mathrm{e},\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{S}\mathrm{n}$, using the augmented-plane-wave (APW) method. Relativistic effects (except the spin-orbit interaction) have been included in each SC cycle, along with corrections to the usual muffin-tin approximation. The latter apply the APW wave functions outside of the muffin-tin spheres to compute the interstitial charge densities and potentials. The resulting interstitial potential has full cubic symmetry (no spherical averaging), although a spherically averaged muffin-tin form is retained inside the spheres. The final SC potentials were used to generate energies and wave functions on a cubic mesh of 35 $\overrightarrow{\mathrm{k}}$ points in $\frac{1}{48\mathrm{th}}$ of the Brillouin zone. These results were interpolated onto a finer mesh of 969 $\overrightarrow{\mathrm{k}}$ points using a symmetrized Fourier method; the densities of states (DOS), $N\left(E\right)\mathrm{}$, were determined using tetrahedral integration. These accurate interpolation methods allow us to determine the DOS on a fine energy scale (±3 mRy) around the Fermi level $E_F$, where we find large variations for the compounds ${\mathrm{V}}_3$Ga, ${\mathrm{V}}_3$Si, and ${\mathrm{Nb}}_3$Sn. This correlates well with the fact that these compounds have high superconducting transition temperatures ($T_c$) and anomalous electronically derived properties. The energy bands of the $A15\mathrm{}$ materials exhibit significant variations even amongst the isoelectronic compounds, both as to band shapes and positions of $E_F$. All compounds possess very flat bands that evolve from the ${\Gamma }_{12}$ state near $E_F$ and give rise to the sharp peaks in $N\left(E\right)\mathrm{}$. For ${\mathrm{V}}_3$Ga, ${\mathrm{V}}_3$Si, and ${\mathrm{Nb}}_3$Sn, $E_F$ falls within several mRy of ${\Gamma }_{12}$ so that these flat bands are responsible for the sharp structure in $N\left(E\right)\mathrm{}$ at $E_F$. We find that ${\mathrm{Nb}}_3$Ge and ${\mathrm{Nb}}_3$Si have relatively low values of $N\left(E_F\right)$, which suggests that the high $T_c\text{'}\mathrm{s}$ observed in films of the former and predicted for the latter are due to unusual mechanisms. We argue that the high $T_c$ in ${\mathrm{Nb}}_3$Ge may be related to soft-phonon modes, disorder, or impurities in the films. Soft x-ray-emission calculations (including matrix elements) of $K$ and $L$ spectra for the vanadium compounds are shown to compare well with experiment. Calculated x-ray photoemission spectra for ${\mathrm{V}}_3$Si, ${\mathrm{Nb}}_3$Ge, and ${\mathrm{Nb}}_3$Sn are also in reasonable agreement with the available data.