Lévy distributions and disorder in excitonic spectra.

We study analytically the spectrum of excitons in disordered semiconductors like transition metal dichalcogenides, which are important for photovoltaic and spintronic applications. We show that ambient disorder exerts a strong influence on the exciton spectra. For example, in such a case, the wellknown degeneracy of the hydrogenic problem (related to Runge–Lenz vector conservation) is lifted so that the exciton energy starts to depend on both the principal quantum number n and orbital l. We model the disorder phenomenologically substituting the ordinary Laplacian in the corresponding Schro¨dinger equation by the fractional one with Le´vy index m, characterizing the degree of disorder. Our v…