Atomic transition region at the crossover between quantum dots to molecules

The presented investigations aim to pinpoint the crossover of lead sulfide (PbS) quantum dots (QDs) with a shrinking diameter to a molecular state. We have measured the transmittance of strongly confined PbS QDs of 2.7, 3.1, 4.7 and 4.8 nm size in the temperature range of 10-300 K. Fitting these results with the classical Fan theory revealed that the average phonon energy coincides with the reduction of the QD diameters, pointing to a limitation of coherent atom movements in strongly confined matter. The phonons vanish at QDs limited to 90 atoms corresponding to a size of 1.7 nm, which we define as the critical size for the solid-to-molecule crossover. The result is confirmed by a calculation based on the uncertainty principle.