Spectroscopic signatures of nonpolarons : the case of diamond

Polarons are quasi-particles made from electrons interacting with vibrations in crystal lattices. They derive their name from the strong electron-vibration polar interaction in ionic systems, that induces associated spectroscopic and optical signatures of such quasi-particles in these materials. In this paper, we focus on diamond, a non-polar crystal with inversion symmetry which nevertheless shows characteristic signatures of polarons, better denoted "nonpolarons" in this case. The polaronic effects are produced by short-range crystal fields with only a small influence of long-range quadrupoles. The many-body spectral function has a characteristic energy dependence, showing a plateau structure that is similar to but distinct from the satellites observed in the polar Fr\"{o}hlich case. The temperature-dependent spectral function of diamond is determined by two methods: the standard Dyson-Migdal approach, which calculates electron-phonon interactions within the lowest-order expansion of the self-energy, and the cumulant expansion, which includes higher orders of electron-phonon interactions. The latter corrects the nonpolaron energies and broadening, providing a more realistic spectral function, which we examine in detail for both conduction and valence band edges.