Symmetrized Fourier method for interpolating band-structure results

Abstract

A method for interpolating band-structure results is described which takes complete account of the translational and rotational symmetry of the crystal. Fourier-series interpolation is used to satisfy requirements of translational symmetry. The effects of band crossings (rotational symmetry) are included in the method by treating each symmetrically different region of the Brillouin zone separately and transferring the results to regions of lower symmetry via the compatibility relations. The method is used to interpolate from a coarse to a finer mesh in $\overrightarrow{\mathrm{k}}$ space where simpler interpolation schemes can be used to determine density of states and Fermi-surface functions accurately. Results of band-structure calculations for several $A15$ structure materials and a monatomic fcc material are used to demonstrate the accuracy and utility of the method.