Integration over the Two‐Dimensional Brillouin Zone

A new method is proposed for the calculation of integrals over the two‐dimensional Brillouin zone (BZ) such as the density of states. The BZ is subdivided into triangles, in which quadratic interpolation over six points for the integrands in wave vector is used, and further subdivision of the BZ into smaller triangles appears to be possible. In each of the “small” triangles obtained the integrals are taken in analytical form on the supposition of linear dependence of integrands on wave vector. Tests of the calculation of the free electron density of states shows quite a high efficiency of the hybrid triangle method.