A note on analytic quadratic Brillouin zone integration

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Abstract
The author proposes an improved quadratic simplex method for evaluating surface and volume integrals in the Brillouin zone. The scheme that is commonly used for deriving a piecewise quadratic interpolation of the dispersion misweights the gridpoints with respect to their symmetry-induced multiplicity. He suggests subdividing the simplices into smaller ones for which different interpolating functions are obtained. In addition, he derives analytical expressions for both the surface and volume integral in two dimensions which properly take into account the integrable Van Hove singularities. As an example, the author discusses the self-consistent calculation of the hole subband structure in a GaAs-AlGaAs heterojunction.