Excitons and Two-dimensional Screening: Critical Screening Lengths

Abstract

A beautiful and intriguing relationship has recently been proposed to express the critical screening lengths associated with the apparition of new bound states for the two-dimensional statically screened Coulomb potential. Semiclassical quantum theory show that this relationship is unfortunately not strictly exact. These results are confirmed by a variational calculation, which provides upper bounds for the critical screening lengths in the case $l\ge 1$.

3 pages; OECS7 conference, Montpellier, France (September 3-7, 2001)