Exciton absorption tails in one-dimensional systems

Exciton absorption tails in direct- and indirect-gap materials are investigated using Toyozawa's exciton self-trapping model as well as Halperin's solution of the random impurity-potential problem. In contrast to the Urbach rule obeyed in two- and three-dimensional systems, the logarithm of the absorption coefficient of a one-dimensional chain is shown to depend on the energy as E3/2, as well as on the inverse temperature T^-1, in accordance with the respective dependences of the density of states in one dimension derived by Halperin.