Excitons and Two-dimensional Screening: Critical Screening Lengths

摘要

A beautiful and intriguing relationship has recently been proposed to expressthe critical screening lengths associated with the apparition of new boundstates for the two-dimensional statically screened Coulomb potential.Semiclassical quantum theory show that this relationship is unfortunately notstrictly exact. These results are confirmed by a variational calculation, whichprovides upper bounds for the critical screening lengths in the case $l \geq1$.