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arXiv · 1306.3702

Exact band structures for 1D superlattices beyond the tight-binding approximation

Olaf Krüger·Alejandro Saenz
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Abstract

The band structures describing non-interacting particles in one-dimensional superlattices of arbitrary periodicity are obtained by an analytical diagonalization of the Hamiltonian without adopting the popular tight-binding approximation. The results are compared with those of the tight-binding approximation. In this way, a quantitative prediction of the validity and failure of the tight-binding approximation becomes possible. In particular, it is demonstrated that in contrast to the prediction of the tight-binding approximation the central energy bands do not touch for periodicities $τ$ of the lattice where $τ=4n$ and $n$ is an integer.

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Olaf Krüger, Alejandro Saenz. 2013-06-16. Exact band structures for 1D superlattices beyond the tight-binding approximation. https://arxiv.org/abs/1306.3702

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