On the existence of Stark ladders in finite crystals

Abstract

The electronic states of a finite crystal in a uniform electric field are studied for a linear, one-band, tight-binding chain with nearest neighbour overlaps, the most favourable case for the existence of a Stark ladder in the energy spectrum. The use of Brillouin-Wigner perturbation theory leads directly to an exact ladder for an infinite chain and strongly suggests that a fraction of the levels arising from atoms in the central part of a finite chain form a weakly perturbed 'quasi-ladder'. The properties of continued fractions enable analysis of finite size effects on the Stark levels of isolated atoms and yield accurate upper and lower bounds for the edges of the perturbed energy spectrum. Detailed numerical calculations substantiate these conclusions.