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

We calculate the two-photon absorption in bulk and single-layer hexagonal boron nitride (h-BN) both by an ab initio real-time Bethe-Salpeter approach and by a real-space solution of the excitonic problem in tight-binding formalism. The two-photon absorption obeys different selection rules from those governing linear optics and therefore provides complementary information on the electronic excitations of h-BN. Combining the results from the simulations with an analysis of the crystal symmetries, we show that two-photon absorption is able to probe the lowest-energy $1s$ state in the single-layer h-BN and the lowest degenerate exciton of bulk h-BN. This result indicates that in h-BN multilayer stackings with inversion symmetry one can measure the Davydov splitting by means of a combination of one and two-photons excitations. The same analysis can be applied to other two-dimensional materials with the same point-group symmetry---such as the transition metal chalcogenides.