Heriot-Watt Mathematics Report Series
HWM00-18, 9 August 2000

Exact Energy Bands and Fermi Surfaces of Separable Abelian Potentials

E D Belokolos, J C Eilbeck, V Z Enolskii and M Salerno


Abstract

We present a general theory for multidimensional Schrödinger equations with separable Abelian potentials with an arbitrary number of gaps in the spectrum. In particular we derive general equations which allow to express the energy and the wave vectors in the BZ as a function of the spectral parameters. By using the solutions of these equations, we show how to construct the energy bands and the Fermi surfaces in the first Brillouin zone of the reciprocal lattice. As illustrative examples we consider the case of 2D separable potentials with 1-, 2-, and 3-gaps in the spectrum. The method can be applied to crystals with a cubic or a rectangular parallelogram Wigner-Seitz cell in arbitrary dimensions. The possibility to generalize the theory to other crystal symmetries is also briefly discussed.

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Publication

E D Belokolos, J C Eilbeck, V Z Enol'skii, M Salerno , Exact energy bands and Fermi surfaces of separable abelian potentials, J. Phys. A: Math. Gen., 34, 943-959, (2001).


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