Calculation of two-photon absorption by nanocrystals of CsPbBr3

We present calculations of the two-photon absorption cross section σ(2)(ω) for nanocrystals (NCs) of the inorganic perovskite CsPbBr3 for photon energies ω ranging from the absorption threshold at 2ω≈2.3eV up to 2ω=3.1eV. The calculations employ a 4×4k⋅p envelope-function model, with final-state excitons described in a self-consistent Hartree-Fock approximation. The k⋅p corrections to σ(2)(ω) are found to be rather large, giving a reduction of about 30% in the cross section at the largest energies considered. The cross section is shown to be independent of polarization in the effective-mass approximation (EMA), but including k⋅p corrections leads to a small difference in σ(2)(ω) between circular and linear polarization, which rises to about 16% at 2ω=3.1eV. The theoretical cross section follows closely a power-law dependence on NC size, σ(2)(ω)∝Lα, with theoretical exponents α=3.4 (EMA) or α=3.2 (4×4k⋅p model), in excellent agreement with experiment. The dominant contribution to the exponent α is shown to be the number of final-state excitons per unit energy. Measured values of the absolute (normalized) cross section σ(2)(ω) show a large spread of values, differing by as much as a factor of 25 for some NC sizes. Our calculations strongly favor a group of measurements at the lower end of the reported range of σ(2)(ω).National Research Foundation (NRF)Published versionThe authors would like to thank Sum T. C. for helpful discussions. They acknowledge the France-Singapore Merlion Project 2.05.16 for supporting mutual visits. T.P.T.N. and S.A.B. are grateful to F. Schuster of the CEA's PTMA program for financial support. C.G. gratefully acknowledges financial support from the National Research Foundation through the Competitive Research Program, Grant No. NRF-CRP14-2014-03