Tetrahedron method of zone integration: Inclusion of matrix elements

Abstract

The tetrahedron method of Brillouin-zone integration is examined in comparison to the rectangular approach. Tetrahedrons are found to be more generally applicable, but they lack the simplicity provided by the symmetry inherent in the rectangular approach. In some earlier calculations of the magnetic susceptibility $\chi (\overrightarrow{\mathrm{q}}, \omega )$ the effect of the variation of the matrix elements throughout the Brillouin zone was not adequately accounted for. A method is described for incorporating this effect within the framework of the tetrahedron method. The possible effect of interpolation on the calculation of spectral functions is also discussed.