Exciton Fine Structure in Lead Salt Nanocrystal Quantum Dots

Lead salt (PbX, X = S, Se, Te) quantum dots (QDs) are widely used in optoelectronics and <i>in vivo</i> fluorescence imaging due to tunability of their fundamental optical transition with the QD size within the near-infrared and mid-infrared ranges. These materials have both conduction and valence band extrema located at the four L points of the Brillouin zone forming four inequivalent anisotropic valleys. This leads to a high degeneracy of the energy spectrum in bulk materials which is partially lifted in QDs, resulting in the exciton fine structure. Understanding and controlling the exciton fine structure in PbX QDs is of key importance for full utilization of their unique optical properties.<br/><br/>We report a tight-binding calculation of the exciton ground-state fine structure in PbS QDs of different sizes and shapes, complemented by a thorough symmetry analysis[1]. We show that the exciton fine structure in PbX QDs is governed by the competition of two main mechanisms [1,2]. One is the electron-hole exchange interaction which can be best understood within the isotropic <b>kp</b> model and is not sensitive to QD shape or valley anisotropy. This interaction has both intra-valley and inter-valley parts and promotes formation of a single ultra-bright state. Emergence of the ultra-bright state is a manifestation of valley coherence which is akin to super-radiance in the reciprocal space. The other competing mechanism is mixing of the valley states due to the scattering at the QD surface. The lower cubic symmetry of the crystal lattice dictates that exciton states from different valleys form combinations representing basis functions of irreducible representations of the symmetry group. While the inter-valley electron-hole exchange interaction tries to arrange the exciton states from different valleys in a fully symmetric combination, valley mixing favors combinations prescribed by the lattice symmetry. Thus, valley mixing distorts the ultra-bright state and leads to redistribution of its oscillator strength among 8 radiative triplets allowed by the symmetry. The radiative triplet having lowest energy is responsible for low-temperature photoluminescence and has radiative lifetime in the microsecond range in agreement with experimental findings. The exciton fine structure splittings between various bright states in core/shell PbS/CdS colloidal nanocrystals have been directly measured by means of single-QD spectroscopy at cryogenic temperatures and are in agreement with the results of our calculations [3].<br/><br/>[1] I. D. Avdeev, M. O. Nestoklon, and S. V. Goupalov, Nano Lett. <b>20</b>, 8897 (2020).<br/>[2] S.V. Goupalov, E.L. Ivchenko, and M.O. Nestoklon, arXiv:2203.10295.<br/>[3] Z. Hu, Y. Kim, S. Krishnamurthy, I.D. Avdeev, M.O. Nestoklon, A. Singh, A.V. Malko, S.V. Goupalov, J.A. Hollingsworth, and H. Htoon, Nano Lett. <b>19</b>, 8519 (2019).