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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