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Construction of a dispersion relation from an arbitrary density of states

The dispersion relations of energy bands in solids are characterized by their density of states, but a given density of states may originate from various band structures. We show how a spherically symmetric dispersion can be constructed for any one-band density of states. This method is applied to one-, two- and three-dimensional systems. It also serves to establish that any one-band spectrum with finite bandwidth can be obtained from a properly scaled dispersion relation in the limit of infinite dimensions.

preprint2002arXivOpen access
Marcus Kollar
cond-mat.str-el
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Marcus Kollar

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