Local Density of States and Level Width for Wannier-Stark Ladders

Abstract

The local density of states ρ(x,E) is calculated for a Bloch electron in an electric field. Depending on the system size, we can see one or more sequences of Wannier-Stark ladders in ρ(x,E), with Lorentz type level widths and apparent spatial localization of the states. Our model is a chain of delta function potential barriers plus a step-like electric potential, with open boundary condition at both ends of the system. Using a wave tunneling picture, we find that the level widths shrink to zero as an inverse power as the system size approaches infinity, confirming an earlier result.