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We calculate the two-photon absorption in bulk and single layer hexagonalboron nitride (hBN) both by an ab-initio real-time Bethe-Salpeter approach andby a the real-space solution of the excitonic problem in tight-bindingformalism. The two-photon absorption obeys different selection rules from thosegoverning linear optics and therefore provides complementary information on theelectronic excitations of hBN. Combining the results from the simulations witha symmetry analysis we show that two-photon absorption is able to probe thelowest energy $1s$ states in the single layer hBN and the lowest darkdegenerate dark states of bulk hBN. This deviation from the "usual" selectionrules based on the continuous hydrogenic model is explained within a simplemodel that accounts for the crystalline symmetry. The same model can be appliedto other two-dimensional materials with the same point-group symmetry, such asthe transition metal chalcogenides. We also discuss the selection rules relatedto the inversion symmetry of the bulk layer stacking.

Two-photon absorption in two-dimensional materials: The case of hexagonal boron nitride