Fig. 5: UCPL mechanism of high-quality QDs.

a Definitions of the average up-conversion energy gain (∆E_avg) and the maximum energy gain (∆E_max) for UCPL. E_ex, E_{PL peak}, E_1S, and E_{PL max} are the energy of the excitation light, the photoluminescence peak, the 1^st excitonic absorption peak and the maximum detected photoluminescence. The above energies are marked on the absorption (black) and photoluminescence (red) spectra. b Measured (black line) and calculated (red squares) absorption spectra normalized at the 1st excitonic absorption peak. The spectrum is calculated according to Eq. S33 in the Supplementary Information. E_1S–E denotes the energy difference of the 1st excitonic absorption peak and the excitation photons. c Schematics of the UCPL mechanism. Shown is one set of electron–phonon coupled states with a specific phonon mode. v is the quantum number of phonon. |G⟩ and |E⟩ are ground and excited states respectively. hv_ex and hv_em denote excitation and emission lights. Inter-band (intra-band) transitions are marked as solid (dashed) arrows.