New three-dimensionalk→·p→model for the electronic structure ofA−15compounds and application to anomalous properties ofV3Si andNb3Sn in the cubic phase

A new three-dimensional $\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{p}}$ model for the electronic structure of $A-15$ compounds is presented. The model is based upon the sixfold degenerate electronic bands with symmetry R(4) of space group $O_h^3$. The Hamiltonian is constructed by using a generalized $\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{p}}$ method: this employs the relevant Clebsch-Gordan coefficients for R(4) $\otimes$ R(4), and simplifications were made to enable calculations to be performed. The density of states obtained shows an enhancement in a relatively narrow energy range. Several physical properties were calculated in the cubic phase with very good agreement with experimental results; these are the temperature-dependent magnetic susceptibility and temperature-dependent shear-mode elastic constant in the range of ${300}^{\circ }\mathrm{K}>T>\mathrm{}{T}_m$. The calculated effect of magnetic field on the shear-mode sound velocity and on the structural transition temperature $T_m$ is in satisfactory agreement with experiment. The tetragonal distortion at $T_m$ is estimated. This model differs from previous models in not using one-dimensionality, quasi-one-dimensionality, or a tight-binding approximation.