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 proportinal 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 \ensuremath{\gamma}=2/ \ensuremath{\surd}6\ensuremath{\pi} ln2 =0.553 by analysis and 0.6 by experiment.