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

TL;DR

This paper investigates how electron-hole pairs form in disordered one-dimensional systems, revealing that both attractive and repulsive interactions can produce states with large localization lengths, similar to two-electron systems.

Contribution

It demonstrates that electron-hole pair states with large localization lengths occur even with weak interactions, using numerical methods and finite-size scaling to analyze their dependence on disorder and interaction strength.

Findings

Large localization lengths for electron-hole pairs with weak interactions

Similarity between electron-hole pairs and two-electron systems in disorder

Dependence of localization length on disorder and interaction strength

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.