Extended Data Fig. 2: Modeling of electronic states and measurements of CdSe/ZnSe/CdS/ZnS QDs.

a, Calculated band-edge transition energy of the CdSe (r = 2.6 nm)/ZnSe (l)/CdS (h)/ZnS (d = 0.3 nm) QDs as a function of l and h. The region within the green boundary corresponds to the regime of well-defined indirect and direct exciton states, as indicated by the electron-hole (e-h) overlap integrals (θ_eh) of <0.1 and >0.9 for the lowest and the first excited e-h states, respectively. The region within the blue boundary corresponds to the regime where we simultaneously satisfy the conditions Δ_d,i = E_d – E_i > k_BT and Δ_id,ii = E_id – E_ii < k_BT (k_B is the Boltzmann constant and T is the temperature; it is assumed that T is 300 K). According to our simulations (Supplementary Note 1), this automatically implies that we also satisfy the condition Δ_dd,id = E_dd – E_id > k_BT. Thus, the region highlighted by the diagonal grey lines corresponds to the QD dimensions for which all requirements necessary for the realization of hybrid direct/indirect biexcitons are satisfied. b-d, Single-dot and ensemble measurements of three CdSe/ZnSe/CdS/ZnS QD samples, the dimensions of which correspond to three different points in the diagram shown in panel a: (b) red open circle (l = 1.7 nm, h = 2.2 nm; same sample as in Figs. 2 to 4); (c) blue open square (l = 1.7 nm, h = 0.7 nm); (d) black open triangle (l = 0.9 nm, h = 2.4 nm). The top row shows single-dot second-order intensity correlation (g⁽²⁾) measurements. The middle row presents the spectrally integrated ensemble PL dynamics measured using low-intensity (sub-single-exciton) pulsed excitation with a photon energy of 2.54 eV. The bottom presents the ensemble PL spectra of the QDs obtained using low-intensity cw excitation with a photon energy of 2.76 eV. The observed characteristics of the samples shown in panels c and d are consistent with those of type-I and quasi-type-II QDs^31,33, respectively.