Abstract

We discuss the spectrum and the eigenfunctions of a 2D Wannier-Stark system in both the tight-binding and single-band approximations. We show that the unfamiliar infinite-variable Bessel functions play a crucial role in these considerations. Furthermore, a closed formula for the eigenfunction for an arbitrary tight-binding ansatz in terms of an expansion in Wannier states is derived. Finally we give a closed form solution for the Wannier-Stark states in the scope of the single-band approximation.

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