Exponential tails near the band edges of a one-dimensional disordered exciton system in the Coherent Potential Approximation

We report the results of studies of the tails near the band edges of a one-dimensional Frenkel exciton system in the Coherent Potential Approximation (CPA). A Gaussian distribution of the transition frequencies with rms width $\sigma $ (0.1 $\le \sigma \le $ 2.0) is used. We found that the tails obey two different exponential power laws depending on the value of $\sigma $. In the weak disorder limit 0.1 $\le \sigma <$ 0.5, the tails of the absorption line shape and the density of states behave like $exp(-k|E|^{3/2} / \sigma^2)$, and in the strong disorder limit,\textit{0.5 $< \sigma \le $ 2.0}, the tails behave like $exp(-|E|^2 / \sigma^2)$. In the weak disorder limit, our CPA results are in excellent agreement with previous investigations.