ORIGIN OF THE STOKES SHIFT - A GEOMETRICAL MODEL OF EXCITON SPECTRA IN 2D SEMICONDUCTORS

We consider the optical absorption and emission spectra of excitons in two-dimensional semiconductors disordered through interface fluctuations. These spectra show a universal behavior exemplified by the fact that the offset of the spectral peaks (the Stokes shift) is proportional to their linewidths over a range of at least 2 orders of magnitude. We introduce a topographical theory of the exciton spectra which models such behavior in terms of statistical properties of a Gaussian random function. The coefficient of proportionality between the Stokes shift and the exciton absorption linewidth is found to be gamma = 2/square-root 6pi ln 2 = 0.553 by analysis and 0.6 by experiment.