Renormalized frequency shift of superradiant excitons in thin semiconductor films

The radiative frequency shift of an exciton in a thin semiconductor film, like its radiative level width, is shown to be superradiatively enhanced. Unlike the latter, however, a finite frequency shift can only be obtained after proper renormalization for the correlated system. The shift is found to be inversely proportional to the square of the factor ${\mathit{k}}_0$d and proportional to the film thickness T, ${\mathit{k}}_0$=${\mathit{E}}_{\mathbf{q}\mathit{n}}$/ħc, ${\mathit{E}}_{\mathbf{q}\mathit{n}}$ being the exciton energy gap and d the lattice constant of the semiconductor. Therefore, the coherent frequency shift can be observed experimentally if one varies the thickness, or the exciton energy gap ${\mathit{E}}_{\mathbf{q}\mathit{n}}$ by imposing high pressure.