The problem of a band electron in a crystal with alternating hoppings is investigated in the presence of a uniform electric field.Exact solutions for the energy spectrum and the wave functions are obtained with the help of SU(2) symmetry.It is found that the energy spectrum contains all orders of the reciprocal of the applied electric field besides the usual Stark ladders.A theoretical analysis shows that in the weak field regime,such nonlinear terms will dominate the localization behavior of the band electron.Only in the strong field regime am the Wannie-Stark localization be observed manifestly.The onset magnitude of the electric field strength for the occurrence of the Wannie-Stark localization is about 2×105V/m for common semiconductor superlattices,which is consistent with experimental observations.
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