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Based on the Bethe-Salpeter equation eigenstates, we present afirst-principles many-body formalism for calculating the two-photon absorption(TPA) coefficient of semiconductors. We apply this formalism to calculate theTPA spectra of MoS2 and WS2 monolayers. The all-electron full-potentiallinearised augmented-plane wave based functions are used for solving theBethe-Salpeter equation. The calculated spectra are in good agreement with theavailable experimental ones for WS2 monolayer. The calculated TPA spectraexhibit significant excitonic effects when compared to those based on theindependent particle approximation. The physical origin of TPA excitonictransitions of MoS2 and WS2 monolayers are revealed by tracing thesum-over-states process. We show that the spin-orbit coupling effect leads tocharacteristic double peaks with an interval of half spin-orbit splittingenergy. These double peaks mainly originate from the transitions at thevicinity of K point.

Excitonic effect on two-photon absorption of two-dimensional semiconductors: Theory and applications to MoS2 and WS2 monolayers