Auger recombination of dark excitons in ${\rm WS_2}$ and ${\rm WSe_2}$ monolayers

We propose a novel phonon assisted Auger process unique to the electronic band structure of monolayer transition metal dichalcogenides (TMDCs), which dominates the radiative recombination of ground state excitons in Tungsten based TMDCs. Using experimental and DFT computed values for the exciton energies, spin-orbit splittings, optical matrix element, and the Auger matrix elements, we find that the Auger process begins to dominate at carrier densities as low as $10^{9-10}~{\rm cm^{-2}}$, thus providing a plausible explanation for the low quantum efficiencies reported for these materials.