Van Hove singularities and zero-slope points in crystals

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Abstract
A method is described for identifying essential stationary points in the electronic energy bands or the lattice vibration spectrum Ej(k) of a crystalline solid with space group G. It is noted that Ej(k), considered as a function of k, possesses the symmetry of a certain symmorphic space group G' and the relationship between G and G' is identified. In addition to essential stationary values it is also possible to identify certain points at which the derivative of Ej(k) vanishes for only a restricted number of directions. The results are tabulated and a comparison is made with the method and results of Kudryavtseva.
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