Existence of Wannier-Stark localization

Abstract

The eigenstates of an electron in an arbitrarily long periodic chain under the influence of an applied electric field are determined. The interaction of the electron with the electric field is divided into two components. The first component has the lattice periodicity and is incorporated into the system's periodic potential. It describes the electric-field-induced alteration of each of the periodic potential wells. The second component, a nonperiodic steplike function, is shown to have vanishing interband matrix elements. Indeed, it produces Wannier-Stark localization with its eigenvalues yielding Wannier-Stark ladders. Thus it is shown that the Wannier-Stark localization survives consideration of multiple electronic energy bands.