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Electron pairing in periodic potentials under an external electric field

We study the semiclassical dynamics of interacting electrons in a biased crystal lattice. A complex dynamical scenario emerges from the interplay between the Coulomb and the external electric fields. When the electrons are far apart, the Coulomb potential may be small compared to the external potential and the electrons oscillate with effective Bloch frequencies, determined by the local electric field. In the opposite case, nearby electrons either separate or form a bound pair, depending on the initial energy compared to the band width. The pair due to the Coulomb field is stable even in the absence of the external field.