Formation of electron-hole pairs in a one-dimensional random environment

Abstract

We study the formation of electron-hole pairs for disordered systems in the limit of weak electron-hole interactions. We find that both attractive and repulsive interactions lead to electron-hole pair states with large localization length ${\lambda }_2$ even when we are in this non-excitonic limit. Using a numerical decimation method to calculate the decay of the Green function along the diagonal of finite samples, we investigate the dependence of ${\lambda }_2(U)$ on disorder, interaction strength $U$ and system size. Infinite sample size estimates ${\xi }_2(U)$ are obtained by finite-size scaling. The results show a great similarity to the problem of two interacting electrons in the same random one-dimensional potential.

15 RevTeX 3.0 pages with 7 EPS-figures included