Perturbative approach to the polaron shift of excitons in transition metal dichalcogenides

In this Letter, we study the effect of phonons on the position of the $1s$ excitonic resonance of the fundamental absorption transition line in two-dimensional transition metal dichalcogenides. We apply our theory to ${\mathrm{WS}}_{2}$, a two-dimensional material where the shift in the absorption peak position has been measured as a function of temperature. The theory is composed of two ingredients only: (i) the effect of longitudinal optical phonons on the absorption peak position, which we describe with second-order perturbation theory, and (ii) the effect of phonons on the value of the single-particle energy gap, which we describe with the Huang Rhys model. Our results show excellent agreement with the experimentally measured shift of the absorption peak with the temperature.