It is shown that arbitrary external fields, and in particular, antibinding ones, bind the Bloch electron in the one-dimensional one-band model. In other words, the spectrum for arbitrary nonzero field is purely discrete and the eigenfunctions are normalizable. This generalizes the Wannier-Stark effects to nonhomogeneous fields.

• Received 7 May 1976

DOI:https://doi.org/10.1103/PhysRevB.16.711