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

抄録

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, T¹ 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 (T²) 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.