Two Classes of Composite Energy Bands in Solids

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Abstract
Composite energy bands are subdivided into two classes. Class-I bands are shown to decompose into a set of simple bands. This is achieved by replacement of the Bloch functions (labeled by the energy) by basis functions that are labeled by the symmetry centers of the band. Because of their decomposition into simple bands, class-I bands have uniquely defined Wannier functions with an exponential falloff. Symmetry arguments are used to prove that Bloch functions of any composite band are necessarily discontinuous.