Numerical Experiments on the Absorption Lineshape of the Exciton under Lattice Vibrations. I. The Overall Lineshape.

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Abstract
A standardized formulation is introduced for the lineshape problem–the effect of lattice vibrations on the exciton absorption, and used in a Monte-Carlo calculation of the density of exciton states and the absorption spectra in the regime of weak scattering. For the direct edge, we obtain the asymmetric lineshape with a strongly decaying low-energy side while the high-energy side can be approximated by a life-time broadened Lorentzian. The linewidth is found to depend on temperature as T 2/3 , T 1 and T 3/2 for one-, two-, and three-dimensional lattices in agreement with renormalized perturbation theory in one and two dimensions. The discrepancy of the perturbational result ( T 2 ) in three dimensions is ascribed to the density of states which is most sensitive to disorder in this case. The shift of the absorption peak is found to be linear in T for low T , the origin of its sublinear behaviour for higher T is clarified.