  The strong Coulomb forces in monolayer transition metal dichalcogenides
ensure that optical excitation of band electrons gives rise to Wannier-Mott
excitonic states, each of which can be conceptualized as a composite of a
Gaussian wavepacket corresponding to center-of-mass motion and an orbital state
corresponding to the motion of the electron and hole about the center-of-mass.
Here, we show that at low temperature in monolayer MoS2, given quasi-localized
excitons and consequently a significant inter-exciton spacing, the excitons
undergo dipole-dipole interaction and annihilate one another in a manner
analogous to Auger recombination. To construct our model, we assume that each
exciton is localized in a region whose length is on the same scale as the
excitonic diameter, thus causing the exciton to behave in a fermionic manner,
while the distance between neighboring excitons is much larger than the exciton
diameter. We construct the orbital ladder operators for each exciton and apply
Fermi's Golden Rule to derive the overall recombination rate as a function of
exciton density.
