Representation of a Lattice Electron in a Uniform Electric Field

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Abstract
Previous authors have applied the crystal‐momentum representation of lattice electrons to various problems involving interband transitions in the presence of a uniform electric field. This representation displays a new set of energy levels (“Wannier‐Stark” levels) which appear to be analogous to the “Landau” levels occuring in a magnetic field. Each level is considered to refer to an individual electron state, as in the case of “Landau” levels. The purpose of the present discussion is to show that “Wannier‐Stark” levels, however, cannot be interpreted as referring to electron states (“Kane” states). The discussion is based on Houston's solution which may be expressed in terms of “Kane” states. It is pointed out that previous calculations of the Franz‐Keldysh effect and Zener tunneling, based on Kane's ideas, contain a contradiction which directly reflects the inconsistency of the “Kane” state picture. However, owing to a tacitly made limiting process, the mentioned theories arrive at the correct results.

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