Impact of electron–phonon interaction on dynamic conductivity of gapped Dirac fermions: Application to single layer MoS2

Single layer MoS2 is a two valleys semiconductor with a direct band gap in the visible. Because it lacks inversion symmetry, circular polarized light can be used to excite charge carriers almost exclusively from a single valley. Here we study how the electron–phonon interaction manifests in this material with gapped Dirac fermions and strong spin–orbit scattering. We find that, not only is the quasi-particle dynamics modified through the usual self-energy term but the gap itself becomes renormalized. Both its real and imaginary part acquire an energy dependence which reflects phonon structure and leads directly, in the longitudinal and transverse (Hall) optical conductivity, to a new peak at twice the phonon energy above the main absorption edge. Phonon assisted Holstein absorption side bands appear in the Hall conductivity even when there is no Drude contribution because of the gap changes and consequently the Berry curvature is modified. While we use parameters specific to the case of MoS2 for illustrative purposes, the theory presented here also applies to other gapped Dirac fermion systems such as those found in topological insulators and silicene.