Comment on ‘‘Existence of Wannier-Stark localization’’

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Abstract
In a recent paper Emin and Hart separated the potential of a constant electric field into two terms: a periodic sawtooth and a staircase. They argued that the sawtooth could be combined with the periodic crystal potential and that the staircase would not induce tunneling between the energy bands of the combined potential. We first show that this would, if true, result in an unresolvable paradox and then point out the subtle mathematical error in their proof. When it is corrected, one finds that the interband matrix elements of the staircase potential are nonzero for any number of unit cells in the crystal, including N→∞.

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