Simple Brillouin-zone scheme for the spectral properties of solids

Abstract

This work is a result of search for an efficient and accurate scheme for the calculation of solid-state properties from the $k$-space integration inside the Brillouin zone (BZ). A survey shows that because of the lack of a satisfactory interpolation method the presently available BZ schemes are either too complicated or too specialized to be desired for accurate and vast applications. A scheme which uses a small number of first-principles $k$ points (∼ 150) to achieve a high accuracy has been obtained. The special feature of the scheme is the utilization of a set of coordinates which allow the interpolation and integration to be carried out in a systematic one-dimensional manner. The problem associated with the band crossing and band switching in real crystals can also be handled easily within the scheme. The quality of the scheme has been satisfactorily tested by a direct comparison of the calculated density of states with the exact results for the tight-binding band models. The electronic density of states for Cu has also been calculated to demonstrate the applicability of the scheme in real crystals. With its simplicity, generality, and accuracy, the present scheme should be very useful for the calculation of various spectral properties of solids. The application of this scheme in the study of impurities and disordered alloys and in connection with the empirical parametrization of the electronic structure of solids is also discussed.