Fig. 4

Direct measurement of the exciton binding energy and Rydberg states in RPPs with n equals 1 to 5. a Optical density OD and photoluminescence excitation PLE spectra of the RPP with n equals to 4 (see the others in Supplementary Fig. 9) clearly showing the exciton ground state 1s and the excited exciton states 2s and 3s. b Corresponding energy of the exciton Rydberg states. Dashed line is a fit to the 2s and 3s states with the 2D hydrogen model²⁶ of exciton Rydberg series using R_y = 0.11 ± 0.04 eV and E_G = 2.078 ± 0.012 eV in the formula E _Ns  = E_G − R_y /(N − 1/2)², with Ns equals to 1s, 2s, 3s. c Evolution of the exciton ground state, first excited state 2s, and continuum energies with the 2D perovskite layer thickness (or n). d Corresponding experimental binding energy of the exciton ground state (1s) and the excited exciton states (2s, 3s, 4s), and comparison to theoretical results for the exciton ground state. The gray open triangle corresponds to the 1s exciton binding energy calculated for the diamagnetic shift obtained by Tanaka et al.¹⁵ in a RPP with n equals to 1 with larger organic spacers (see Fig. 1d, e). The values E_1s − E_2s provide a lower limit for the exciton binding energy. Error bars correspond to s.d. from the determination of the energy of the exciton features