Excitonic two-photon absorption in monolayer transition metal dichalcogenides: Impact of screening and trigonal warping

Two-photon spectroscopy is an important tool for detection of states that are dark in single-photon spectra. We calculate two-photon absorption spectra for monolayer transition-metal dichalcogenides including excitonic effects based on a Bethe-Salpeter equation approach. Both spin-orbit coupling and trigonal warping are included. Our results reveal that otherwise dark p states dominate the two-photon response. However, weakly allowed two-photon transitions coinciding with single-photon s-state resonances appear due to trigonal warping. The angular momentum character of participating excitons is analyzed and we study the sensitivity to screening by dielectric surroundings and discuss the free-carrier limit. Biexciton contributions to the high-energy two-photon response are estimated using a simplifiedWannier approach. Finally, a brief comparison with recent experiments is given.