A formula for calculating the interband matrix elements of X for a Bloch electron in a uniform electric field is derived, from which it is found that the interband matrix elements of X are only determined by the interband matrix elements of the derivative of the periodic potential. Using this formula with a Kronig-Penney potential leads to nonvanishing interband matrix elements of X in a general setting, which implies that the exact Stark-ladder structure cannot exist in solids.

• Received 18 February 1992

DOI:https://doi.org/10.1103/PhysRevB.46.1305