Quantum coupling in colloidal homodimers of epitaxially attached CdSe@CdS dot@platelets probed on single-particle level

Domain: physics
Published: 2026-02-18
Editorial outcome: major_revision

Abstract
Coupled quantum-dot (QD) dimers can be viewed as diatomic artificial molecules, thus offering a unique platform to study molecular physics and quantum phenomena. However, controlled synthesis of QD dimers has remained an outstanding experimental challenge, given necessary construction of hundreds of lattice bonds at the neck between two QDs with a unique attachment axis. Here, QD homodimers are synthesized in solution with a high yield by the epitaxial attachment of two monodisperse CdSe@CdS dot@platelet QDs along their common <1120> axis. The exact construction of hundreds of lattice bonds in the epitaxial neck are enabled by the large (1120) side facets with ideal lattice match between two epitaxial QDs and limited ligands passivation, resulting in controlled spacing between two core QDs (core-spacing). Single-particle spectroscopy reveals that the photoluminescence (PL) of single homodimer with a small core-spacing (7.8 nm) is split into two room-temperature resolvable peaks, consistent with strongly-split bonding and antibonding electron orbitals of “artificial diatomic molecules”. The two peaks of the split PL are orthogonally-polarized, and two types of molecular biexcitons are observed for the homodimer. These advancements lay a viable foundation for controllable construction of “artificial molecules” in solution.

Introduction
Atom-like electronic states1–3 makes semiconductor nanocrystals with strong quantum confinement (quantum dots, QDs) known as “artificial atoms”, which are in rapid development as an integral part of a semiconductor platform for photon manipulation4. If two (or a few) QDs are quantum-coupled through single-crystalline neck(s) to form molecule-like electronic states, they should be named as “artificial molecules”5–7. Similar to regular molecules, molecule-like properties of “artificial molecules” would be mostly observed at the band edges as bonding and antibonding frontier orbitals. These engineered molecular architectures serve as the probes for fundamental quantum phenomena and versatile candidates for advancing quantum-enabled devices8–10. However, the molecule-like properties of diatomic artificial molecules (e.g., homodimers) fabricated via molecular-beam epitaxy (MBE) on single-crystalline substrates currently remain resolvable solely under cryogenic conditions8,9,11–15. This is so because the splitting energy between the bonding and antibonding orbitals of an MBE-grown homodimer is only 1–5 meV5,16–18, which is about one order of magnitude smaller than the thermal energy at ambient temperature (≈25 meV). The orbital hybridization of colloidal “artificial molecules” with the controlled coupling strength could be pronounced and resolvable at room temperature. However, colloidal “artificial molecules” are currently blocked by a few synthetic challenges, despite extensive efforts since the 1990s6,7,19–22.

For MBE-related epitaxial technologies and solution chemistry, challenges for formation of “artificial molecules” with room-temperature detectable molecule-like properties come from different ways. MBE growth of homodimers—the simplest “artificial molecules”—needs to generate a vast amount of identical yet independent symmetry-breaking sites at an atomic level on a single crystalline substrate. As for the construction of complex “artificial molecules” (such as trimers and tetramers), symmetry-breaking sites on the single crystalline substrate must be in a well-organized pattern at an atomic level, which is prohibitive at present. Furthermore, because of the stringent epitaxy conditions through MBE, all existing combinations of single crystalline substrate and epitaxial structure are limited to those with small confinement energy for the atom-like states, and the resulting energy split between the bonding and antibonding orbitals of a homodimer would thus be small and uncontrollable5,16–18.

Since the 1990s, colloidal synthesis of nanocrystal dimers and trimers through attachment in solution has been actively explored through ligands-linking23–26 and DNA templating27–29. While these approaches demonstrated a solution to stable chemical connection of a fixed number of nanocrystals, the organic linkers would unlikely establish coherent quantum coupling between two/three inorganic nanocrystals. The challenging issue of inorganic crystalline fusion of two nanocrystals after assembly on silica beads30,31 was finally solved in the 2010s, which illustrated some interesting optical properties with the crystalline fused homodimers of two CdSe/CdS core/shell QDs31–36. This last strategy made a step forward to yield nanocrystal homodimers with solely inorganic neck for each QD dimer, the hetero-facet attachment of the polycrystalline neck, i.e., either non-epitaxially or epitaxially-attached along a random selected axis, remains as next major challenge. With the hetero-facet attached homodimers, extensive optimization of core spacing, neck dimension, and core size31,32,35 does not offer strong evidences for identifying molecular bonding and antibonding states. For instance, all detectable emissions of dual-peak PL of single CdSe/CdS dimer were assigned to two uncoupled QDs33. Time-resolved single-particle spectroscopy measurements confirmed that two emission states were either the single-exciton emissions of two QDs with slightly different emission energy or combination of one neutral exciton and one trion state. Two peaks of such dual-peak (or multi-peak) PL of a dimer would possess either similar polarization angle or randomly-oriented transition dipole, consistent with two quantum-uncoupled QDs10,33.

Besides attachment, direct epitaxial growth of one quantum system on top of another with barriers between each other has also been explored37–41, which are mostly based on CdS/HgS/CdS37 and CdSe/Cd(Zn)S/CdSe core/well/shell quantum wells38, CdSe@CdS dot@rod QDs39,40, and type-II CdTe/CdS/CdSe core/shell/shell QDs41. Albeit grown with epitaxy, two (or multiple) quantum systems in a colloidal nanocrystal did not demonstrate bonding and anti-bonding molecular orbitals, likely because their QD (and/or quantum well) and barrier dimensions were difficult to be optimized into the necessary geometry19,21,22. As shown by theoretical calculations, quantum coupling is highly sensitive to the size of two quantum systems, the properties of the barrier (or neck), the epitaxial-attachment direction, and the dimensions of the epitaxial neck6,19–22,42.

Here, we hypothesize that, with nearly monodisperse core size and shell thickness, epitaxial fusion of two single-crystalline core/shell QDs along a common axis in solution may lead to ideally monodisperse “artificial diatomic molecules”. We understand that this strategy needs to navigate a few additional challenges to realize strong coherent quantum coupling. Firstly, the attachment should be not only epitaxial but also facet-selective, given the quantum coupling is sensitive to epitaxial-attachment direction. Secondly, to form an epitaxial neck with desirable dimensions, the facet-selective attachment requires the precise construction of hundreds of chemical bonds with a fixed lattice axis between two nanocrystals. Thirdly, the epitaxial neck must allow quantum coupling to form a “artificial molecule”, instead of either merging two QDs into a large “artificial atom” or isolating two QDs as two independent quantum systems. Fourthly, optical properties of the initial QDs and resulting epitaxial-attached dimers must be sufficiently defined for identifying the molecular states. Following these guidelines, the faceted wurtzite CdSe@CdS dot@platelet QDs43 with a low dispersity in size are chosen for establishing the solution strategy. In comparison with spheroidal CdSe/CdS core/shell QDs31 with a low dispersity in size, two large polar basal facets, i.e., (0001) and (0001), are bonded with strong ligands and should thus be inert for attachment. Conversely, their nonpolar (1120) and/or (1010) side facets are relatively large and flat, dynamically passivated with weak ligands44, which might thus be selectively accessible for epitaxial attachment with a defined neck. The optical properties of CdSe@CdS dot@platelet QDs are nearly unity PL quantum yield, mono-exponential PL decay dynamics, nearly non-blinking at a single QD level, and a two-dimensional emission dipole (spherically polarized)43, ideal for studying coherent quantum coupling between two nanocrystals.

Results
Facet-selective attachment epitaxially along the <1120> axis
The pre-synthesized CdSe@CdS dot@platelet nanocrystals43 (Supplementary Fig. 1) are added into an epitaxial-attachment solution—dodecylamine (DoNH2, 25 vol.%) and octadecylamine (OdNH2, 25 vol.%) as dynamic45 and entropic46 ligands in octadecene (50 vol.%)—at 280°C (Fig. 1a). After 5-h reaction under the given conditions, the conversion ratio from the nanoplatelet monomers to homodimers for the optimized reactions can reach 50%-60%, and it is ≈30% in average for all reactions studied. Through typical size-selective precipitation47, the population of the homodimers can be consistently improved to 80–90% (Supplementary Fig. 2), with about 70–80% recovery ratio of the dimers in the specific fraction. The overall conversion ratio of the nanoplatelets to homodimer through an optimized reaction/separation procedure can be as high as 35–45%.

High-resolution transmission electron microscope (TEM) measurements reveal that the epitaxial attachment through the scheme in Fig. 1a is solely along the <1120> axis of the wurtzite lattice (Fig. 1b-e), indicating suitable facet-selective and epitaxial attachment. Provided each (1120)-attached homodimer with two large basal planes, all homodimers in Fig. 1b show clear cross fringes, and selective-area electron diffraction (SAED) of a large number of homodimers deposited on the TEM substrate shows a common <0001> zone axis (Fig. 1c). Along the <0001> zone axis, width of the epitaxial necks (Fig. 1b, d) is approximately 1/3 of that of the nanoplatelet for the specific sample. Occasionally, the homodimers are with their <1010> zone axis perpendicular to the TEM substrate, revealing the neck thickness being about the same as that of the QD building blocks (Fig. 1e). Elemental distribution along the <1120> axis (Supplementary Fig. 2) is in good accordance with the homodimer configuration.

Formation of trimers (Fig. 1f-h) and tetramers (Supplementary Fig. 2) is not the goal of the current work and thus limited to a small portion under the optimized conditions. These complex structures can be isolated in the first fraction of the size-selective separation. Importantly, these complex nanostructures are also (1120)-attached with characteristic bond angles as 180o, 120o, and 60o, suggesting that the solution chemistry for epitaxial attachment is robust and can produce complex “artificial molecules” not easily accessible for the MBE technology.

Epitaxial attachment along the <1010> axis
Results above suggest that the epitaxial attachment through the reaction scheme in Fig. 1a is facet-selective solely towards the nonpolar (1120) side facets, instead of the nonpolar (1010) side facets and the polar basal planes. To understand this selectivity, the CdSe@CdS dot@platelet nanocrystals are facet-reconstructed in a solution to form hexagonal-nanoplatelets with their side facets being solely (1010) ones44 (Fig. 2b and Supplementary Fig. 3). An optimized epitaxial-attachment scheme (Fig. 2a) only yields 10%-20% of homodimers, yet the homodimers are indeed epitaxially attached along the wurtzite <1010> axis (Fig. 2c, d and Supplementary Fig. 3). Different from the (1120) attached ones, the neck(s) of a (1010)-attached dimer (or a trimer/tetramer) usually consists of only one monolayer of atoms with some point defects (Fig. 2c–g and Supplementary Fig. 3), and the neck thickness terminates at the end of the attached (1010) facets (Fig. 2d).

Overall, successful synthetic schemes for a given type of designated homodimers not only depend on the starting materials (see above) but also the type and concentration of ligands, reaction temperature, reaction time, and concentration of the QDs. Dynamic amine ligands for the (1120)-attachment and small cadmium carboxylate (cadmium acetate, Cd(Ac)2) ligands for the (1010)-attachment are necessary to allow formation and sufficient exposure of the designated facets. Excessively high ligand concentrations would provide over-protection for the designated facet(s) and hinder the attachment, thereby reducing the dimer yield. Conversely, overly low ligand concentrations would rapidly destabilize the nanocrystal solution and lead to uncontrolled aggregates with randomly-oriented, polycrystalline, and/or multi-nanocrystal attachments. High temperatures (above 280°C) often cause inter-particle and intra-particle ripening48, and insufficient thermal agitation would not induce precise construction of hundreds of chemical bonds along a designated and common lattice facet between two nanocrystals.

Exclusion of epitaxial attachment of the polar facets including the (0001), (0001), and the (1011) facets—the (1011) ones available for the hexagonal-nanoplatelets as the slope facets connecting the (0001) basal plane and side facets (see Fig. 2d)—should be a result of their tightly-bonded surface ligands44. Such strong ligands would form a closely-packed monolayer of hydrocarbon chains on the given facet and act as a kinetic barrier under the mild epitaxial-attachment conditions. Selection among the two nonpolar side facets for the epitaxial attachment, i.e., the (1120) facets over the (1010) ones, should be a result of their atomic packing patterns49. Supplementary Fig. 4 shows that, ideal for epitaxial attachment, either cation or anion on a (1120) facet is always has a single dangling bond. Conversely, a nonpolar (1010) facet is terminated with both monodentate and bidentate cations/anions that require a special anion-cation matching between two nanoplatelets for the epitaxial attachment, specifically, “monodentate anions to monodentate cations” and “bidentate anions to bidentate cations” for the construction of hundreds of lattice bonds. This stringent requirement may also cause the appearance of a noticeable amount of point defects in the thin (single monolayer) neck of the (1010)-attached dimers, trimers, and tetramers.

In comparison with a relatively small (1120) facet of the original nanoplatelet monomers43, the neck dimensions of the homodimer, including its thickness, width, and length (Fig. 1b–d) are large. This suggests that the chemical bonds between two epitaxially-fused QDs should have followed a typical two-step-oriented attachment studied by in-situ TEM50,51. In the first step, two QDs follow the site-selective coalescence at two relatively small (1120) facets to form a facet-selective neck with a small cross-section (Supplementary Fig. 4). In the second step, the surface atoms would move to the low-energy neck area through the known facet-reconstruction process in the given solvent system44.

Control on core-spacing of homodimers for quantum coupling
The scheme in Fig. 1a can be readily applied for the synthesis of the (1120)-attached homodimers with various core-spacing in high yield (Fig. 3a and Supplementary Fig. 5). Experimentally, the CdS shells with a designated thickness are epitaxially grown onto CdSe core nanocrystals with a given size (≈3 nm)43. The resulting CdSe@CdS dot@platelet nanocrystals with three different CdS shell thicknesses along the lateral direction (i.e., 2.4, 3.3, and 4.2 nm) are isolated, each of which is dissolved in octadecene at room temperature in the reaction flask. Subsequently, each reaction solution is heated up to 280 oC under Ar atmosphere, into which the DoNH2-OdNH2 entropic and dynamic ligands are introduced for the facet-selective attachment (Fig. 3a). All spectroscopy measurements below are carried out at room temperature. Statistically, the homodimers for the three samples in Fig. 3a are with about the same neck cross section (4.7 nm width and 7.0 nm thickness), which means precise formation of about 200 Cd-S epitaxial bonds at the attached (1120) facet for each homodimer. Though the CdSe core size is 3 nm for all three samples, the nearly monodisperse core-spacing dictated by the CdS shell lateral thickness increases from 7.8, 9.6, to 11.4 nm from top to bottom in Fig. 3a.

Figure 3b demonstrates that, regardless of the differences on the core-spacing, main features of UV-vis spectra of all three samples remain observable after epitaxial attachment, excluding formation of a large “artificial atom” by complete fusion of two QDs. Consistent with theoretical predictions for “artificial diatomic molecules”6,19–22,52, red-shift and broadening of the band-edge UV-vis absorption peak, red-shift of PL peak, and absorbance increase in the high-energy region relative to the first excitonic absorption peak are all apparent for the homodimers with the smallest core-spacing (top plot in Fig. 3b) and observable to a certain degree for those with the median core-spacing (middle plot in Fig. 3b). Conversely, UV-vis and PL spectra (Fig. 3b, bottom plot) for the homodimers with the largest (11.4 nm) core-spacing are nearly identical to those of the corresponding monomers, indicating two QDs within a homodimer in this sample remain as two independent “artificial atoms” with any possible quantum coupling observable at room temperature. For simplicity, the one with smallest core-spacing shall be denoted as “diatomic molecules” below while those without any evidence of quantum coupling shall be named as “double-QDs”.

Single-particle spectroscopy of <1120>-attached homodimers
TEM-correlated single-particle spectroscopy53 (Supplementary Fig. 6) is adopted here for studying a single diatomic molecule with single QD monomer and a single double-QD dimer as the references. Figure 4a reveals similar PL counts for a single monomer, diatomic molecule (7.8 nm core-spacing), and double-QD (11.4 nm core-spacing) after normalization by the number of QDs in each emitter. The TEM-correlated spectroscopy measurements suggest that this unified intensity level can be applied as a simple indicator to distinguish the residual monomers from the dimers in a given sample. Figure 4a further illustrates that all three PL intensity trajectories are nearly free of dim states (Fig. 4a) and statistically qualified as non-blinking54 (Supplementary Fig. 7). In some cases, a single diatomic molecule can exhibit a PL intensity trajectory with a significant number of dim states generated by blinking, which offers a possible way to study optical properties of the dim states (Supplementary Fig. 8). The optical properties described below, including those of single-exciton and biexciton, are for the bright state (or the neutral QD) unless otherwise specified.

While the PL spectrum of single monomer shows a single Lorentzian peak (Fig. 4b, top), single homodimer with the smallest core-spacing (7.4 nm) possesses dual-peak PL (Fig. 4b, middle), which is distinctly divergent from a single yet broad PL peak exhibited by hetero-facet attached homodimers of the spheroidal CdSe/CdS core/shell QDs31,32. Conversely, the PL spectrum of a double-QD (core-spacing 11.4 nm) is nearly identical in its contour and peak width with the corresponding monomer (Fig. 4b bottom). Within statistical error (Supplementary Fig. 9), all double-QD spectra can be well-fitted with a single Lorentzian peak, similar to that of the single monomer, consistent with two independent QDs in a double-QD. Given the original monomers of two reactions with similar ensemble-PL peak width (Fig. 3b top and bottom), results of double-QD measurements—each with a single Lorentzian peak—suggest that the commonly-observed dual-peak PL of a single diatomic molecule should not be a result of emissions from its two independent QDs in a homodimer.

Within the statistical error, each homodimer with the smallest core-spacing (7.8 nm) judged by the TEM-correlated spectroscopy and/or the unified-intensity indicator (50-60 in total for a specific sample) shows the dual-peak PL, each of which can be deconvoluted into two peaks, i.e., PL1 and PL2 in Fig. 4b (middle). The splitting energy between PL1 and PL2 (ΔE) of 50-60 diatomic molecules of the specific sample is 36.4 ± 11.0 meV (Supplementary Fig. 10). The intensity ratio between PL1 and PL2 of the diatomic molecules follows a Boltzmann distribution55 (Fig. 4c), in accordance with single exciton emission from two split electron levels that are accessible through thermo-equilibrium56–60. Statistical results reveal that, relative to the corresponding monomer’s PL peak at 2.014 ± 0.020 eV, PL1 and PL2 exhibit blue-shift to 1.999 ± 0.018 eV and red-shift to 2.036 ± 0.021 eV, respectively (Supplementary Fig. 10). These results are in agreement with the electron bonding and antibonding energy level splitting caused by quantum coupling between two QDs in a homodimer.

The PL decay lifetime of single diatomic molecule remains nearly constant across different PL intensity fractions and at different PL emission wavelengths (Supplementary Fig. 11), supporting dual-peak PL originating from two split electron levels in thermo-equilibrium55–60. Transient PL measurements (Fig. 4d) reveal a double-channel PL decay dynamics for a single diatomic molecule with a much-increased average lifetime (40 ns, ensemble PL quantum yield as 68%) relative to the corresponding monomer (25 ns, ensemble PL quantum yield as 97%), implying the unlikelihood of emissions from two independent QDs in a dimer. Conversely, the PL decay dynamics of a single double-QD—determined as a dimer emitter by the two indicators—and its corresponding monomer are nearly identical (Supplementary Fig. 12), in accordance with two independent QDs in a double-QD. Presumably, the relatively low PL quantum yield of a typical sample of diatomic molecules could be due to the subpopulation of trimers (8%), given a purified trimer sample always with a very low PL quantum yield (<10%). In addition, possible defects in the epitaxially-attached neck area of diatomic molecules could cause delayed photoluminescence with a somewhat reduced PL quantum yield and quasi-double channel PL decay49.

Results in Fig. 3b and Fig. 4a–c all suggest that quantum coupling of the band-edge electron atomic orbitals (1S(e)) likely exists between two QDs in a homodimer with a small (7.8 nm) core-spacing (see Fig. 3a), which would form the band-edge bonding and antibonding electron orbitals (or molecular states)5,6,19–22,42,52 (Fig. 4e). Because of the deep valence band of the epitaxial CdS neck and large hole effective mass of CdSe, two band-edge hole levels (1S3/2(h)) in the two cores would remain as two localized nonbonding orbitals6,19–22,52 (Fig. 4e). The average splitting energy ΔE (≈35 meV) between PL1 and PL2 is in the same magnitude of the bonding-antibonding splitting energy predicted for diatomic molecules with similar dimensions in ref. 19, though the exact value of energy splitting between bonding and antibonding electron orbitals is under debate42. It should be noted that the homodimers discussed in this subsection are all epitaxially-attached along the <1120> axis that is different from those often considered in the literature6,19–22. In addition, all calculations in the literature were based on spherical CdSe/CdS core/shell QDs, the coupling energy of which may differ from that for homodimers of CdSe@CdS dot@nanoplatelet QDs. Presumably, largely different spatial distributions of the photo-generated electron in either bonding or antibonding molecular orbital and hole in a localized orbital of either core reduces their wavefunction overlapping roughly by a half, leading to a much elongated single-exciton radiative decay lifetime.

Albeit measured at cryogenic temperatures61, two transition dipoles involving a localized hole state and either bonding or antibonding molecular electron state of a diatomic molecule grown by MBE have been confirmed to be perpendicular to each other. With its <0001> axis perpendicular to the substrate, the PL intensity of a single monomer remains unchanged upon rotating the polarization angle of detection (inset, Fig. 4b top), consistent with a two-dimensional dipole on a plane parallel to the basal planes of a CdSe@CdS dot@nanoplatelet43. On the contrary, either PL1 or PL2 of a diatomic molecule is linearly polarized (see raw data in Supplementary Fig. 13) at room temperature, with their transition dipoles perpendicular to each other (Fig. 4f). The orthogonally-polarized dual-peak PL is distinctively different from a pair of emission peaks resolved at cryogenic temperatures of a single hetero-facet attached homodimer of two spheroidal CdSe/CdS core/shell QDs33. Although the mechanism of orthogonally-polarized dual-peak PL is unclear, it at least suggests that the two PL peaks are very unlikely from emissions of two uncoupled QDs in a dimer, provided the distinctive polarization of a monomer (inset, Fig. 4b top).

Except correlation with the molecular bonding and anti-bonding orbitals, the dual-peak PL of single diatomic molecule could also be caused by three other mechanisms, namely, size variations of the two QDs in single diatomic molecule, Förster resonance energy transfer arising from size dispersity24, and charged-exciton states (i.e., trion)62. Figure 1 shows that the lateral dimensions of CdSe@CdS dot@nanoplatelets are somewhat broad, which is known to affect optical uniformity less than their better-controlled thickness43. In addition, the single Lorentzian peak emission of single double-QD (Supplementary Fig. 9), the polarization measurements in Fig. 4b (inset, top plot) and Fig. 4f, the much increased PL decay lifetime (Fig. 4d), and the Boltzmann distribution of peak areas of the two peaks based 50–60 dimers (Fig. 4c) all suggest that the dual-peak PL would be unlikely from two independent QDs in a dimer. Statistical results for ≈50 single QD and ≈50 early-termed single diatomic molecules are summarized in Supplementary Fig. 10. The Statistic results illustrate that the average energy position of the PL peak of single QD is between those of the two peaks of dual-peak PL, and the distribution profile of the high-energy (or low-energy) peak for dual-peak PL extends significantly beyond the low-energy (or high-energy) end of single QD, respectively. These results are against either simple size variation or Förster resonance energy transfer arising from size dispersity of two QDs in a homodimer with the smallest core-spacing in Fig. 3a.

Results in Supplementary Fig. 8 and Fig. 4c exclude the possibility of the dim-state emission (i.e., trion emission of singly-charged nanocrystal) as the high-energy PL2 in Fig. 4b (middle). Instead of a blue-shifted peak, the trion-state spectrum of single diatomic molecule shows a similar dual-peak PL with a minute red-shift of both peaks (Supplementary Fig. 8). In comparison with the bright-state emission, the PL2/PL1 intensity ratio of the dim-state emission of single diatomic molecule increases slightly due to increased thermal population of the antibonding orbital55–60. PL decay dynamics of the trion emission can be well fitted with mono-exponential function with a very short lifetime (≈6.6 ns, Supplementary Fig. 8). Such a short lifetime is expected for the trion state from a QD with strong nonradiative Auger recombination63. As mentioned above, the dual-peak PL in Fig. 4b (middle) shows no sign of contribution from this short-lifetime channel in the entire intensity range (Supplementary Fig. 11), disapproving significant contribution from trion-state emission. In addition, it is difficult to imagine the intensity ratio between the dim- and bright-state emissions follow the Boltzmann distribution observed in Fig. 4c.

Biexciton properties of the <1120>-attached homodimers
“Artificial molecules”, including diatomic ones, are expected to demonstrate the special molecular biexciton properties36,63,64. For single QD monomer, the second-order photon intensity correlation (g(2)) measurement (Fig. 5a, top) reveals a typical g(2) contrast—equivalent to the biexciton emission quantum yield relative to that of single-exciton for single quantum emitter65—as ≈0.05 (see statistics in Supplementary Fig. 14). Figure 5a (middle) demonstrates that, for single homodimer with the smallest core-spacing in Fig. 3a—early-termed as diatomic molecule, a modest increase of the typical g(2) contrast (≈0.25), with an average of 0.26 (see statistics in Supplementary Fig. 14). This mild increase of biexciton quantum yield is expected for a diatomic molecule (see below).

Contrary to early-termed diatomic molecule, the g(2) contrast surges to a value as high as ≈0.83 for a typical double-QD (Fig. 5a, bottom) and an average of ≈0.6 without counting the atypical ones (Supplementary Fig. 15), excluding dominant contributions from biexciton emission in a single quantum emitter. Theoretically, within the strongly quantum confined size regime (i.e., with strong nonradiative Auger recombination), the g(2) contrast of two independent QDs in a double-QD could be calculated as g(2)=(1+QYXX/QYX)/2 ≈ [1+QYXX(1+kNR/kr)]/2 under weak excitation34. Here, quantum yields of biexciton and single-exciton by exciting either QD in a double-QD dimer are respectively denoted as QYXX and QYX, and kNR and kr represent the rate constants of nonradiative and radiative decay of its single exciton, respectively. With the values of QYXX and QYX, the calculated g(2) contrast is close to the average g(2) contrast of the double-QD. The atypical g(2) could be a result of occasional excessively low single-exciton QYX due to accelerated nonradiative decay by formation of a double-QD.

The micro-liquid film approach is applied for studying excitation power-dependence of ensemble PL (Methods section) to avoid the influence of photo-ionization of the QDs63. Results (Supplementary Fig. 16) confirm that the QD monomers in a micro-liquid film show a biexciton PL decay channel (≈0.9 ns) with ≈5% PL quantum yield, consistent with the biexciton properties of CdSe/CdS core/shell nanocrystals with a similar core size and shell thickness63,64. Similar ensemble measurements using the micro-liquid film approach reveal distinctive features for the early-termed diatomic molecules in their steady-state and transient PL spectra of biexcitons. Figure 5b, c demonstrates that a long-lived biexciton (lifetime ≈4.8 ns) with relatively high quantum yield (≈26%) becomes visible by just increasing the average photon absorption per pulse (<N>) to 1.0. Further increase of <N> to ≈3.0 makes another biexciton decay channel (lifetime ≈1.4 ns, quantum yield ≈5%) detectable (see detail in Supplementary Fig. 17). It is interesting to notice that, though one of the biexciton channels possesses high PL quantum yield (≈26%) and should contribute significantly to the total emission at relatively high excitation power, the normalized steady-state PL spectra for the entire series (Fig. 5d and Supplementary Fig. 18) barely vary from the single-exciton spectrum.

All results about biexcitons for the homodimers with the smallest core-spacing can be interpreted using the band-edge energy diagram of diatomic molecule in Fig. 4e, which leads to a simplified scheme for its band-edge single-exciton in Fig. 5e, i.e., with the electron in either bonding or antibonding state and the hole in one of two uncoupled core states. In this molecular diagram, there would be two types of distinguishable biexcitons in a diatomic molecule. If two holes are separately localized on two epitaxially-attached core QDs in a diatomic molecule (Fig. 5f), there would be only one effective Auger nonradiative recombination channel. Specifically, one spatially-delocalized electron in either bonding or antibonding orbital and one localized hole recombine and pass the energy to the other spatially-delocalized electron. Given the bonding and antibonding electron states being delocalized in both QDs in a homodimer, this would result in suppression of the Auger nonradiative recombination in comparison with that in the corresponding monomer. As a result, if the homodimers with the smallest core-spacing in Fig. 3a would be diatomic molecules, a long biexciton decay lifetime (4.8 ns) and an increased relative quantum yield (26%) for the molecular biexciton state would be observed in comparison with the corresponding monomers. Different from this electron-delocalized and hole-segregated molecular biexciton (sBX), the two holes of the second molecular biexciton state (cBX) are colocalized in one of the two epitaxially-attached core QDs in the diatomic molecule (Fig. 5g), activating the other Auger nonradiative decay involving two holes. Similar to single (3 nm) CdSe monomer63, the two holes colocalized in the same CdSe core QD result in highly efficient Auger nonradiative recombination. This would make the cBX behave almost the same as the biexciton of the corresponding monomer within the experimental accuracy, namely, a low biexciton quantum yield (5%) with a short lifetime (1.4 ns). The biexciton decay lifetime of the cBX (1.4 ns) is slightly longer than that of the corresponding monomer (0.9 ns), which should be a result of the relaxed Auger nonradiative decay involving two electrons of the cBX. As a result, the g(2) contrast of a single diatomic molecule would be dominated by the long-lifetime biexciton sBX (Fig. 5a, middle).

According to Fig. 5b, c, contributions to the total PL from the molecular biexciton cBX are negligible (<5%) within the excitation power range. The wavefunction configuration of the long-lifetime molecular biexciton (sBX, Fig. 5f) is almost the same as that of either single-exciton (Fig. 5e) or the corresponding trion, implying the same dual-peak contour with slightly different PL2/PL1 intensity ratio for these three states. Thus, the different PL2/PL1 intensity ratio and subtle peak shift are irresolvable for the ensemble steady-state PL spectra recorded under various excitation intensity (Fig. 5d). This conclusion is also consistent with theoretic calculations36, which predicted that biexciton binding energies of the sBX and cBX biexciton states of homodimers with similar dimensions should be ≈0 meV and ≈35 meV, respectively.

Methods
Materials
Cadmium oxide (CdO, 99.99%), cadmium acetate dihydrate (Cd(Ac)2·2H2O, 98.0%), selenium power (100 mesh, 99.99%), 1-octadecene (ODE, 90.0%), trioctylphosphine oxide (TOPO, 90.0%), octylamine (OcNH2, 99.0%), oleylamine (OlNH2, 70.0%), dodecylamine (DoNH2, 98.0%), octanoic acid (HOc, 98%), oleic acid (HOl, 90%) and poly(methylmethacrylate) (PMMA, average Mw≈120,000 g mol-1 by gel permeation chromatography) were purchased from Sigma-Aldrich Corporation. Trioctylphosphine (TOP, 90%), sulfur powder (sublimed, −100 mesh particle size, 99.5%) and octadecylamine (OdNH2, 97.0%) were purchased from Alfa-Aesar. Tributylphosphine (TBP, 95%) was purchased from Acros. All organic solvents were purchased from Sinopharm Chemical Reagents. All the chemicals were used as received without further purification.

Synthesis of (1120) attached homodimers with different core spacing
The CdSe@CdS dot@platelet nanocrystals were used as starting materials to prepare homodimers. The CdSe@CdS dot@platelet nanocrystals with different lateral dimensions and the same thickness were synthesized and purified according to ref. 43. OdNH2 (25 vol.%) and DoNH2 (25 vol.%) were dissolved in 3.0 mL of ODE and degassed under argon atmosphere at 160°C for 10 min and heated to 280°C, the purified pre-prepared nanoplatelets in ODE (1.0 mL) were injected into the flask. The mixture was stirred at 280°C for 5 h under an argon atmosphere, and then the reaction mixture was allowed to cool down to room temperature. The resulting homodimers were precipitated with methanol and dispersed in 2.0 mL toluene.

Isolation and purification of (1120) attached homodimers
To obtain the purified homodimers, the gradient precipitation method was used to separate the as-synthesized homodimers. The ethyl acetate and acetone (2.0 mL, volume ratio, 1:1) with the addition of free ligands (OcNH2 (50 µL), OlNH2 (50 µL) and TOP (100 µL)) as a precipitation reagent for gradient centrifugation. Consequently, by dropwise adding the precipitation reagent into the solution of as-synthesized homodimers and the precipitation for many times, and many cycles of size selective precipitation, yielding a sample with 80–90% nanoplatelets in the form of homodimers reproducibly.

Surface treatment of (1120) attached homodimers and the corresponding monomers
The surface treatment of the isolated monomers and homodimers according our previous work with a slight modification43,67. OlNH2 (1.0 mL) was dissolved in 1.0 mL of ODE and degassed under argon atmosphere at 160°C for 10 min. After cooling down the mixture to 110°C, the isolated monomers or homodimers in ODE (1.0 mL) and 1.0 mL S-ODE (0.1 mol L-1, dissolving sulfur powder in ODE) were successively injected into the flask. The mixture was stirred at 110°C for 20 min, and then, the nanocrystals were precipitated by methanol. This sulfur treatment process was repeated until no fluorescence of the nanocrystals was detected, indicating that the nanocrystals were completely treated with sulfur. After completion of the sulfur treatment, 0.2 mL TBP was added into the reaction mixture at 220°C. After 3 min, the reaction mixture was allowed to cool down to room temperature, and Cd(Ac)2 (0.2 mL, 0.1 mol L-1 in OcNH2) was added dropwise into the solution. Subsequently, the sample was irradiated under a 395 nm LED until the surface traps of the nanocrystals were fully removed.

Synthesis of (1010) attached homodimers
The CdSe@CdS dot@platelet nanocrystals were used as starting materials to prepare the homodimers with (1010) facets attachment. Cd(Ac)2·2H2O (0.08 mmol) was added to 0.4 mmol of DoNH2 and 0.4 mmol of OdNH2, the mixture was stirred at 100°C for 15 min, until a colorless solution was obtained. In a three-neck flask, 2.0 mL of ODE was degassed under argon atmosphere at 120°C for 10 min and heated to 220°C, the above colorless solution of Cd(Ac)2 in fatty amines, and the purified pre-prepared nanoplatelets in ODE (1.0 mL) were successively injected into the flask. The mixture was stirred at 220°C for 1 h under argon atmosphere, and then the reaction mixture was allowed to cool down to room temperature. The resulting (1010) attached homodimers were precipitated with methanol and dispersed in 2.0 mL toluene.

Optical measurements and structural characterization for ensemble nanocrystals
For all measurements in solution, toluene was chosen to be the solvent. Absorption spectra were measured using an Agilent Technologies Cary 4000 UV-visible spectrophotometer. Steady-state and transient PL spectra were performed on an Edinburgh Instruments FLS920 spectrometer. The transient PL spectra were acquired on a time correlated single-photon counting (TCSPC) module of the same spectrometer with a 405 nm ps-pulsed laser at a repetition frequency of 0.2 MHz. The absolute PL quantum yield was measured using a calibrated Ocean Optics FOIS-1 integrating sphere coupled with a QE65000 spectrometer. All optical measurements were performed at room temperature. As described in the main text, the biexciton properties of monomers and homodimers can be accurately measured with micro-liquid film approach. The micro-liquid film of monomers and homodimers are made by sandwiching ≈10 μm thick samples solution between two pieces of cover glass. Under a low repetition frequency (1 MHz), the nanocrystals in the micro-liquid freely diffusing in and out the beam area would avoid interference of potentially charged nanocrystals during the saturation measurements. Furthermore, all micro-liquid measurements were performed with a low repetition frequency (1 MHz) to avoid artifacts in the decay traces recorded by TCSPC. An oil-immersion objective with numerical aperture of 1.49 is used to focus the excitation light to the center of the samples micro-liquid film and collect the emission signals for both steady-state and transient PL measurements. Samples were prepared by drop-casting dilute toluene dispersions onto copper grids (400-mesh) coated with a pure carbon support film. Transmission electron microscopy (TEM) images were acquired on a Hitachi 7700 transmission electron microscope with an acceleration voltage of 100 kV. High-resolution TEM images and selective-area electron diffraction (SAED) patterns were collected by a JEM2100F transmission electron microscope operated at 200 kV. High-angle annular dark field (HAADF) image and energy dispersive spectroscopy (EDS) line of the homodimer were obtained using the JEOL JEM-F200 high-resolution transmission electron microscope operated at 200 kV. The dimensions of the samples were quantified via the Nano Measurer.

Optical measurements for a single nanocrystal
Diluted samples solution in toluene with 2.5 wt.% PMMA was spin-casted on a clean glass coverslip for single particle measurements. Spectroscopic properties of single nanocrystal and micro-liquid films were measured using a modified inverted epifluorescence microscope (Olympus IX83) with a 60× oil immersion objective (NA=1.49) and suitable spectral filters under ambient conditions. The 405 nm continuous-wave laser (PicoQuant) was used as an excitation light source, the emission signal of a single nanocrystal can be imaged and recorded by an EMCCD camera (Andor iXon Ultra 897). The steady-state PL spectra were recorded using an Andor Kymera 193i spectrometer, the integration time for each PL spectrum was 2 s. The polarized emitted light of single nanocrystal can also be guided to the spectrometer after passing through a motorized λ/2 wave plate and an additional polarizer. For time-resolved PL measurements, the 405 nm laser was switched to a pulsed mode with a 1 MHz repetition frequency. The emission signals from a single nanocrystal were collected and recorded with an avalanche photodiode (PicoQuant, τ-SPAD). The PL decay traces of single nanocrystal and micro-liquid films were measured using a time-correlated single-photon counting system in the time-tagged time-resolved mode. With different excitation power densities for liquid films, a series of PL decay traces were obtained, and thus the biexciton lifetime and QY could be calculated. Second-order photon correlation measurement was performed with a Hanbury Brown and Twiss setup with two avalanche photodiodes. For single nanocrystal measurements, the average photon number (〈N〉) absorbed was kept below 0.1 to ensure single-exciton emission unless otherwise mentioned. The visualization and fitting of all spectroscopic data were performed using Microsoft Excel or Origin.

Correlation of optical and TEM measurements
The optical measurements of a single homodimer are confirmed by the correlating fluorescence microscopy and TEM. Diluted monodisperse SiO2 microspheres (size: 1 μm) in toluene were spin-casted on copper grids (200-mesh) coated with pure formvar supporting film as markers (large particles in optical and TEM images in the first row in Supplementary Fig. 6) to correlate spectroscopic and TEM measurements for a single homodimer. The pure formvar film was used as the optical and TEM substrate, because this film is transparent in TEM and shows a low fluorescence background. A diluted solution of the homodimers in toluene with 2.5 wt.% PMMA was spin-casted on the pure formvar supporting film, then the spectroscopic properties of a single homodimer were measured using a modified inverted epifluorescence microscope. After all relevant spectroscopic data were collected, the samples were examined by the Hitachi 7700 transmission electron microscope with an acceleration voltage of 100 kV. TEM was performed after the fluorescence measurements to avoid sample contamination and degradation.

Model of emission saturation for micro liquid film approach
Calculation of biexciton QY from the PL saturation curve is according to the published methods64. Here, we consider that single monomer constituent of the homodimers is independent for the light absorption process, the photon number absorbed per monomer per excitation pulse is considered as a Poisson distribution:
P(m,<N>) = (<N>^m * e^(-<N>)) / m!, m=0, 1, 2, 3 (1)
where <N> is the average number of photons absorbed per monomer per pulse.
At a given excitation, the total PL intensity measured from monomer can be written as
I = Σ(m=1 to 1) P(m,<N>) Σ(N=1 to 1) QYmX (2)
where QYmX is the quantum yield of the mexciton state.
Only single exciton emission of monomer is observed at long delay time (e.g., 20–30 ns), when multi-exciton recombination completes. As excitation power increases, the single exciton emission intensity saturates of monomers following the function
I = QY_X * (1 - P(0,<N>)) = QY_X * (1 - e^(-<N>)) = QY_X * (1 - e^(-Cμ)) (3)
where P(m,<N>) is a Poisson distribution function; QY_X is the single exciton quantum yield; C is the scaling factor depending on the absorption cross section; μ is the excitation power. Considering QY_X is unity for high quality monomer sample, C and thus the x axis <N> can be determined by fitting the single exciton PL saturation curve with the function above.
The total emission intensity saturation curve is essential a function of QY_X (QY_BX) and <N>. Fitting the total emission saturation curve in Supplementary Fig. 16 with the model above, the biexciton quantum yield for monomers was determined as QY_BX = 0.05. Due to the lower quantum yield of multiple excitons, only PL emission of single exciton and biexciton is considered here.
For single exciton emission of homodimers, when single monomer constituent of the homodimers absorbs photons (one or more), the hole localized on either of the two attached monomers, and the electron is thermally distributed in the two spatially-delocalized molecular orbitals. The probability can be calculated via the opposite of this event (both of monomer constituent do not absorb photons). As excitation power increases, the single exciton emission intensity saturates of homodimers following the function
I = QY_X * (1 - P(0,<N>)^2) = QY_X * (1 - e^(-2<N>)) = QY_X * (1 - e^(-2Cμ)) (4)
where QY_X is the single exciton quantum yield; C is the scaling factor depending on the absorption cross section of monomers; μ is the excitation power. Considering QY_X is unity for high quality homodimer sample, C and thus the x axis <N> can be determined by fitting the single exciton PL saturation curve with the function above (Fig. 5c).
For biexciton emission of homodimers, two holes separately localized on two epitaxially-attached monomers (Fig. 5f), the electrons are delocalized in the whole homodimers, which is called electron-delocalized and hole-segregated biexciton (sBX). Each monomer must absorb a photon or more. The corresponding emission intensity IsBX can be written as follows:
IsBX = QY_sBX * (1 - P(0,<N>))^2 = QY_sBX * (1 - 2e^(-<N>) + e^(-2<N>)) (5)
When the two holes of the second biexciton state are colocalized in one of two epitaxially-attached monomers (Fig. 5g), the electrons delocalized in the whole homodimers. The electron-delocalized and hole-colocalized biexciton (cBX) involves at least two photons absorbed by one monomer. The opposite event is that both two monomers absorb fewer than two photons. The corresponding emission intensity IcBX can be written as follows:
IcBX = QY_cBX * (1 - (P(0,<N>) + P(1,<N>))^2) = QY_cBX * (1 - (e^(-<N>) + <N>e^(-<N>))^2) (6)
Fitting the saturation curve of sBX and cBX in Fig. 5c with the model above, the quantum yield of sBX and cBX for homodimers are 0.26 and 0.05, respectively.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Lei et al. describe a new synthesis of colloidal QD molecules based on CdSe/CdS dot-in-plate components. The clear advantage vs. past work by the Banin group is that they show well-controlled epitaxial relations upon coupling of QD pairs, augmented by the capability to form larger lattices, including triplets and higher oligomers. Overall, the work is clearly interesting and timely. Nonetheless, there are quite a few issues arising with the optical measurements and their interpretation. Further, the introduction appears to overlook a lot of the past evolution. As such, the manuscript requires significant revision prior to publication. Detailed comments follow.\n1. The authors seem to overlook a lot of literature which predates the growth of \"artificial molecules\" by fusion of two separately grown QDs. These include a variety of core/shell/shell designs starting from CdS/HgS/CdS/HgS/CdS double well structures (Weller), through CdSe/CdS/CdSe core/well systems (by the same lead author as this paper), to PbSeS/CdS/CdSe (Oron, Klimov). They also include double-tipped CdSe or CdS nanorods. All of these, unlike what is stated in the manuscript, do exhibit epitaxial relations. This is not to say that any of these exhibited similar properties as the ones reported here, but overlooking them completely distorts the discussion in the introduction and makes it appear that colloidal coupled QD systems have only been studied by nanocrystal fusion.\n2. The authors quite conveniently ignore the fact their \"diatomic molecules\" exhibit significant temporal variations in emission intensity (Fig. 4a). These insinuate that there is more than one emitting state, and possibly the particles undergo charging-neutralization cycles during the experiment. Can the authors refute the idea that the second emission peak arises from such a charged state, for example? Also - what fractions of what the authors call \"molecules\" exhibit dual emission peaks? Is that a criterion for determining them as \"diatomic molecules\"?\n3. Recent work by the Banin group has emphasized the role of small heterogeneity between the pair of QDs comprising the molecule in determining its emission properties. Here, this parameter is completely absent from the discussion. Why? Could it be that the two emission peaks are associated with two slightly different energies for transitions where the carriers are localized on one of the two dots or on two transitions where one is spatially direct (electron and hole localized on the same dot) and the other is \"indirect\" (electron and hole localized on different dots) so that the exciton binding energy is significantly modified?\n4. Are the results presented here regarding the \"anti-bonding state\" backed by computations showing that this is the expected energy range for the bonding-antibonding energy difference?\n5. The authors report a lifetime of 40ns for the molecule emission but the curve appears to be not single exponential. This is more in line with heterogeneity in the system. Again, this needs an explanation.\n6. For the text it is not clear if the dipole orientation measurements of Fig. 4f are at RT or at low temperature.\n7. The measured g(2) values are not in line with the explanation. going from 0.05 to 0.83 cannot be explained simply by a transition from one to two independent emitters. There has to be coupling there.\nAll in all, the manuscript provides explanations for the observations, but does not really deal with the question of whether these are the only reasonable ones or even the most plausible ones. This has to be remedied to warrant publication in Nature Communications.", "reviewer_2": "In the manuscript entitled “Monodisperse quantum-dot dimers unlocking molecular states at room temperature”, Lei and colleagues demonstrate a generalizable synthetic strategy to prepare dimers and higher order structures of epitaxially fused colloidal quantum dot structures and present compelling evidence for electronic coupling of the QD states at room temperature. The authors develop QD fusion chemistry which is distinct from existing approaches and provides much improved control over the attachment facet and uniformity compared to the established silica sphere templated synthesis method. The electron microscopy data presented supports their claim of highly uniform and controlled facet specific fusion. I believe this is a considerable synthetic advance for the fused QD field in terms of material quality. In addition, the authors show comprehensive optical characterization of the fused quantum dots demonstrating signatures of delocalized electronic states. Given the quality of the results and impact it will have synthetic nanomaterials chemistry and nanoscale optoelectronic communities, I believe it is suitable for publication in Nature Communications.\nWith that said, I have some broad suggestions for improving this manuscript which should be addressed before publication.\n1) Throughout the manuscript the authors claim that all the bonds in the neck must form simultaneously to achieve epitaxial fusion. There is no evidence presented to support this claim. Further, there is considerable evidence in the literature that epitaxial fusion can be achieved thorough a necking process (For Example: Science 2012, 336 (6084), 1014–1018 and Science 2012, 336 (6077), 61–64). The authors should have a more nuanced discussion about the mechanism considering the above manuscripts (and many others on this topic) so that all possibilities are discussed, and readers are not mislead by strong unsupported claims about the mechanism.\n2) I worry about the yield of the process? Can the authors comment on the yield?\n3) In Figure 3, the authors show structural characterization of dimers where they have varied the spacing of the QD cores. From the figure, the description in the caption and main text it is not clear to readers how this was achieved. I infer that the authors synthesized nanocrystals with different shell thicknesses, then these were attached, resulting in dimers with different core-to-core spacing. However, this was not explicitly stated anywhere in the manuscript.\n4) For the discussion on the interpreting the single particle PL and PL decay dynamics, the authors only consider uncharged excitonic states and do not include charged states (Trions, etc.). Is this a good assumption? For single QDs, these charged electronic states are important for interpreting data such as blinking. The authors should provide commentary to justify omitting the consideration of charged species in their analysis or they should consider them in their analysis.\n5) The QD molecules show lower QY compared to the monomers. I can’t help but wonder how the QY decrease of the dimers is manifested. Are all the QD molecules in the ensemble lower QY? The single particle PL and intensity traces would suggest not as there is no off time and thus, they are high QY. Is it possible that the QD molecules which showed the dislocations at the interfaces are completely dark? Not sure if the authors have the data to parse this, nor do they need to given the current scope, but would be worth pointing out.\n6) For fluence dependent TCSPC using the micro-liquid technique, authors should confirm that all measurements were done with appropriately low count rates for TCSPC to avoid artifacts in the decay traces and note this in the methods section.", "reviewer_3": "The present manuscript reports interesting synthetic advances whereby colloidal CdS platelets containing nearly-monodisperse CdSe quantum dots (QDs) are attached laterally, so as to form dimers, trimers or tetramers. This is a potentially important step forward in the development of 'artificial molecules', built by tunnel-coupling electrons confined in nearby quantum dots. I would be pleased to recommend publication of this work in Nature Communications if the authors provide compelling evidence that the work is a significant advance with respect to previous attempts of building artificial molecules out of core/shell CdSe/CdS quantum dots (Ref.31 and ensuing studies, such as Refs. 6,8,19,21,22,33-37). I list my specific concerns and suggestions below.\n1- Please make clear what is the morphological advantange of the present system as compared to that of Ref.31 to produce dimers.\n1.1-The dimensions of the CdSe QDs and the QD-to-QD distances are similar here and in Ref.31, and so are the absorption and PL redshifts at room temperature (up to 9 meV in Fig.3b, 13.5 meV in Ref.31).\n1.2- Lines 36-38 state that artificial molecules with monodisperse geometric dimensions have not been reported before. Does this mean that the monodispersity of dot-in-platelets is higher than that of dot-in-dots? If so, please compare data from the two systems. Ref.34 (cited in line 62) may not be very representative: it seems the authors intentionally chose heteronuclear QDs to simplify the analysis of trion location.\n1.3- Perhaps the orientation of the piezoelectric field (c-axis) is different and matters?\n2- The TEM-correlated single-molecular spectroscopy of Fig.4 is a very interesting probe for this system. However, I have concerns regarding the origin of the dual-peak PL.\n2.1- The double peak may simply reflect emission from the left and right QDs, which are likely not identical. In dimers, the non-radiative relaxation to the largest QD would induce a redshift as compared to monomers (where no such relaxation is possible), and it could be consistent with a Boltzmann thermal distribution.\nI would be more convinced if a systematic correlation of \"Delta E\" (the energy splitting between PL1 and PL2) was observed as a function of the dot-to-dot distance. The three instances of Ref.4b are insufficient.\n2.2- Also, Ref.46 shows dual-peak PL but it has no molecular coupling. Is that mechanism blocked here?\n3- The interpretation provided in Fig.4e (and lines 184-186) seems speculative at this stage. An electron tunneling energy of few tens of meV cannot compete against exciton binding energies of few hundred meV. In CdSe/CdS QD molecules, it was shown that the latter traps the electron next to the hole, which is localized in the CdSe QD, thus preventing delocalization along the neck (see e.g. Chem. Mater. 2024, 36, 11676). Why is it different here?\n4- The orthogonally polarized dual-peak PL is interesting, but its origin should be clarified. The polarization properties are generally related to the periodic (Bloch) part of the wavefunction, rather than the envelope one (which is that affected by molecular tunneling). Ref.52 is cited in the manuscript, but there the changes in polarization were a consequence of suppressing the exciton fine structure (which involves the Bloch part of the wavefunction). Is the fine structure playing a role here?\n5- Similar to point 3, the interpretation of biexciton (BX) emission in Figs.5e-g misses the influence of Coulomb interactions. Not only is electron-hole attraction expected to drag electrons into the CdSe QD, but also hole-hole repulsions are expected to make the configuration of Fig.5g very energetic. Its emission should appear blueshifted with respect to that of Fig.5f. Yet, Fig.5d shows no shift of BX with respect to X. Can the authors estimate biexciton binding energies for different emission channels?\nWhy does the BX behave differently from that of Ref.37, where the two BX decay channels were simply associated to one X in each QD, or two X in the same QD?\n6- More technical comments:\n6.1- What is the temperature in the single-molecule spectra of Fig.4? If it is room temperature, why is the Boltzmann distribution not giving a ratio of 1 for energy splittings of 24 meV (thermal equilibrium is claimed in line 174)?\n6.2- Can the lifetime of PL1 and PL2 be disentangled? If molecular effects play a role, the radiative decay of PL2 should be longer lived than that of PL2 (because bonding orbitals have more charge in the barrier)."}, "author_response": "RESPONSE TO REVIEWERS\nof “Monodisperse quantum-dot dimers unlocking molecular states at room temperature” by Hairui Lei,\nHaiyan Qin, Haixin Lei, Yuqing Wang, Jiongzhao Li, Xiaogang Peng\nResponses to the comments from Reviewer 1:\nGeneral comments: Lei et al. describe a new synthesis of colloidal QD molecules based on CdSe/CdS dot-in-plate\ncomponents. The clear advantage vs. past work by the Banin group is that they show well-controlled epitaxial relations\nupon coupling of QD pairs, augmented by the capability to form larger lattices, including triplets and higher oligomers.\nOverall, the work is clearly interesting and timely. Nonetheless, there are quite a few issues arising with the optical\nmeasurements and their interpretation. Further, the introduction appears to overlook a lot of the past evolution. As such,\nthe manuscript requires significant revision prior to publication. Detailed comments follow.\nAll in all, the manuscript provides explanations for the observations, but does not really deal with the question of\nwhether these are the only reasonable ones or even the most plausible ones. This has to be remedied to warrant\npublication in Nature Communications.\nResponse: Thanks for your appreciation of our work. We have made numerous changes in the manuscript to address\nthe issues.\nComment 1: The authors seem to overlook a lot of literature which predates the growth of \"artificial molecules\" by\nfusion of two separately grown QDs. These include a variety of core/shell/shell designs starting from\nCdS/HgS/CdS/HgS/CdS double well structures (Weller), through CdSe/CdS/CdSe core/well systems (by the same lead\nauthor as this paper), to PbSeS/CdS/CdSe (Oron, Klimov). They also include double-tipped CdSe or CdS nanorods. All\nof these, unlike what is stated in the manuscript, do exhibit epitaxial relations. This is not to say that any of these exhibited\nsimilar properties as the ones reported here, but overlooking them completely distorts the discussion in the introduction\nand makes it appear that colloidal coupled QD systems have only been studied by nanocrystal fusion.\nResponse: Sorry for missing this aspect of the development. Yes, we are aware of these interesting studies. In a way,\nvarious theoretical studies suggested that formation of “artificial molecules” require strong control of core (small) and\nneck (thin) dimensions, which is usually not the case for those references mentioned above. However, we agree that these\npioneering explorations represent epitaxial connection of two or more “artificial atoms”. In the revised manuscript, we\nexpanded the introduction to include discussion on this specific type of QD systems (line 68-73, page 4): “Besides\nattachment, direct epitaxial growth of one quantum system on top of another with barriers between each other has also\nbeen explored38-42, which are mostly based on CdS/HgS/CdS38 and CdS/CdSe/CdS39 core/well/shell quantum wells,\nCdSe@CdS dot@rod QDs40,41, and type-II CdTe/CdSe core/shell QDs42. Albeit grown with epitaxy, two (or multiple)\nquantum systems in a colloidal nanocrystal don’t demonstrate bonding and anti-bonding molecular orbitals, likely\nbecause their QD (and/or quantum well) and barrier dimensions are difficult to be optimized into the necessary geometric\nrange19,21,22.”\nComment 2: The authors quite conveniently ignore the fact their \"diatomic molecules\" exhibit significant temporal\nvariations in emission intensity (Fig. 4a). These insinuate that there is more than one emitting state, and possibly the\nparticles undergo charging-neutralization cycles during the experiment. Can the authors refute the idea that the second\nemission peak arises from such a charged state, for example? Also - what fractions of what the authors call \"molecules\"\nexhibit dual emission peaks? Is that a criterion for determining them as \"diatomic molecules\"?\nResponse: Thanks for these important comments. It’s true that there could be a sufficient number of dim states in an\nintensity trajectory of single “diatomic molecule”, which show emission properties expected for the dim states.\nImportantly, steady-state spectrum, transient PL spectrum, polarization measurements, and bi-exciton measurements\ndeposited in the main text are exclusively with the bright states. To clarify the concerns pointed out by the Reviewer, we\nadded experimental data for single “diatomic molecule” with a sufficient number of dime states as Supplementary Fig.\n8, which demonstrates distinctive steady-state and transient PL spectra of both bright and dim states. In the main text,\ntwo sentences were added to clarify the steady-state and transient PL spectra in the main text are exclusively from the\nbright-state (Line 193-196, page 9-page 10): “In some cases, single diatomic molecule can exhibit a PL intensity\ntrajectory with a significant number of dim states generated by blinking, which offers a possible way to study optical\nproperties of the dim states (Supplementary Fig. 8). The optical properties described below, including those of single-\nexciton and bi-exciton, are for the bright state (or the neutral QD) unless otherwise specified.”\nDiscussion on distinction of the dual-peak emission of the bright states and emission of the dim states was added in the\nrevised manuscript (line 266-277, page 13): “Results in Supplementary Fig. 8 and Fig. 4c exclude possibility of the dim-\nstate emission (i.e., trion emission of singly-charged nanocrystal) as the high-energy PL in Fig. 4b (middle). Instead of\n2\na blue-shifted peak, the trion-state spectrum of single diatomic molecule shows a similar dual-peak PL with a minute\nred-shift of both peaks (Supplementary Fig. 8). In comparison with the bright-state emission, the PL /PL intensity ratio\n2 1\nof the dim-state emission of single diatomic molecule increases slightly due to increased thermal population of the\nantibonding orbital54-59. PL decay dynamics of the trion emission can be well fitted with mono-exponenital function with\na very short lifetime (~6.6 ns, Supplementary Fig. 8). Such a short lifetime is expected for the trion state from a QD with\nstrong nonradiative Auger recombination62, but the PL decay dynamics is starkly different from the bright-state PL. As\nmentioned above, the dual-peak PL in Fig. 4b (middle) is the bright-state emission of intensity trajectory for single\ndiatomic molecule, which shows no sign of contribution from this short-lifetime channel in the entire intensity range\n(Supplementary Fig. 11). In addition, it is difficult to imagine the intensity ratio between the dim- and bright-state\nemissions follows Boltzmann distribution in Fig. 4c.”\nYes, dual-peak PL might be applied as a criterion for determining the diatomic molecule though we chose different\nindicators. After the size-selective precipitation, the yield of diatomic molecules in a sample is typically 80~90%,\nand all\nnanocrystals are with high PL QY. Under single-molecular spectroscopy, the diatomic molecules are distinguished from\nthe residual monomers through the correlated TEM-spectroscopy measurements and the unified intensity level indicator.\nThe unified intensity level indicator relies on the intensity level of the bright states in a PL intensity trajectory. With that\nof single monomer determined using a pure monomer sample under the same measurement conditions as the reference,\nnanocrystal emitters in a diatomic molecules sample are found to be in two categories, namely, the majority (diatomic\nmolecule) with about twice intensity counts of the reference and the rest (residual monomer) with the same intensity\ncounts of the reference. One sentence was added to clarify these standards in the revised manuscript (Line 190-192, page\n9): “The correlated TEM-spectroscopy measurements suggest that this unified intensity level can be applied as a simple\nindicator to distinguish the residual monomers from the dimers in a given sample.” Measurements confirm that each\ndiatomic molecule judged using these indictors would show dual-peak PL. One sentence was added in the revised\nmanuscript (Line 209-210, Page 10) to state this fact: “Experimentally, each diatomic molecule judged by the correlated\nTEM-spectroscopy measurements and/or the unified-intensity indicator (50~60 in total for a specific sample) shows the\ndual-peak PL.”\nComment 3: Recent work by the Banin group has emphasized the role of small heterogeneity between the pair of QDs\ncomprising the molecule in determining its emission properties. Here, this parameter is completely absent from the\ndiscussion. Why? Could it be that the two emission peaks are associated with two slightly different energies for transitions\nwhere the carriers are localized on one of the two dots or on two transitions where one is spatially direct (electron and\nhole localized on the same dot) and the other is \"indirect\" (electron and hole localized on different dots) so that the\nexciton binding energy is significantly modified?\nResponse: This is why we emphasize the optical quality of the monomers for synthesizing the dimers, i.e., high and\nreproducible PL QY with narrow emission peaks, 2D dipole emission determined by the nanoplatelet shape, mono-\nexponential PL decay dynamics with a defined lifetime. High optical quality of the monomers coupled with monodisperse\nattachment structures (facet-selective, fixed neck thickness, and controlled neck length) should remove inhomogeneity\nobserved by the Banin group. Along with their dual-peak PL, the Banin group actually also reported random polarization\norientations of the two peaks, which is consistent with the heterogeneity-induced dual-peak PL. In our experiments, in\nthe control sample of the double-QD dimers (dimers without bonding-antibonding splitting), emission of each double-\nQD is confirmed to be single Lorentzian peak (Fig. 4b, bottom), and all of single double-QD steady-state (Supplementary\nFig. 9) and transient (Supplementary Fig. 12) PL spectra are practically the same as the corresponding monomer.\nTo address this issue, a short paragraph was added to the Introduction in the revised manuscript (Line 58-66, page 3) to\nillustrate the limitations of the Banin’s approach: “However, despite extensive optimization of core spacing, neck\ndimension, and core size in the hetero-facet attached homodimers31,33,36, dual-peak PL of single homodimer observed\nusing single-molecule spectroscopy is inconsistent with those associated with molecular bonding and antibonding states.\nFor instance, at cryogenic temperatures, all detectable states of single CdSe/CdSe dimer are assigned to two uncoupled\nQDs34. Specifically, time-resolved single-molecule spectroscopy measurements confirm that multiple emission states are\neither the single-exciton emissions of two QDs with slightly different emission energy or combination of one neutral\nexciton and one trion state. Furthermore, two peaks of such dual-peak (or multi-peak) PL of a dimer would possess either\nsimilar polarization angle or randomly-oriented transition dipole, consistent with two quantum-uncoupled QDs10,34.”\nIn addition, a few sentences were inserted into the appropriate places to exclude dual-peak PL induced by the size\ndispersion. Revised manuscript Line 202-207 (page 10): “Statistically (Supplementary Fig. 9), all double-QD spectra\ncan be well-fitted with single Lorentzian peak similar to that of single monomer (Fig. 4b top), consistent with two\nindependent QDs in a double-QD. Given the original monomers of two reactions with similar ensemble-PL peak width\n(Fig. 2b top and bottom), results of double-QD measurements—each with single Lorentzian peak—strongly suggest that\nthe commonly-observed dual-peak PL of single diatomic molecule should not be a result of emissions from its two\nindependent QDs.” Revised manuscript Line 249-253 (page 12): “The orthogonally-polarized dual-peak PL is\ndistinctively different from a pair of emission peaks resolved at cryogenic temperatures of single hetero-facet attached\nhomodimer of two spheroidal CdSe/CdS core/shell QDs34, illustrating advantages of the facet-selective attachment\ndisclosed here. The orthogonally-polarized dual-peak PL further suggest that two PL peaks are very unlikely from\nemissions of two uncoupled QDs in a dimer, provided the distinctive polarization of a monomer (inset, Figure 4b top).”\nFinally, this issue is addressed systematically in the revised manuscript (Line 258-264, page 12-page 13): “The size\ndispersity in single diatomic molecule can be excluded by the single Lorentzian peak of single double-QD (Supplementary\nFig. 9), the polarization measurements in Fig. 4b (inset, top plot) and Fig. 4f, the much increased PL decay lifetime (Fig.\n4d), and the Boltzmann distribution of peak areas of the two peaks based 50-60 dimers (Fig. 4c). Förster resonance\nenergy transfer arising from size dispersity might reduce the peak area of the high-energy peak and roughly explain the\nBoltzmann distribution, but could not be consistent with the single Lorentzian peak of single double-QD, the much\nincreased (Fig. 4d) and wavelength-independent PL decay dynamics (Supplementary Fig. 12), and polarization of the\ntwo peaks.”\nComment 4: Are the results presented here regarding the \"anti-bonding state\" backed by computations showing that\nthis is the expected energy range for the bonding-antibonding energy difference?\nResponse: Yes, the observed splitting energy is inline with theoretical calculations. Theoretical calculations in Ref.\n21 (J. Chem. Phys. 2022, 157, 134502) predict that (0001) and (101̅0) facet-connected CdSe/CdS core/shell homodimers\n(2.8 nm core diameter, 7 nm total diameter, 5 nm neck width) exhibit bonding and antibonding orbital splitting energies\nof ~25 meV and ~15 meV, respectively.\nComment 5: The authors report a lifetime of 40 ns for the molecule emission but the curve appears to be not single\nexponential. This is more in line with heterogeneity in the system. Again, this needs an explanation.\nResponse: The experimental results don’t support the long lifetime (40 ns) of diatomic molecule is from size\nheterogeneity of its two independent QDs, which can be addressed from three aspects. One, the lifetime of diatomic\nmolecule is so much longer than that of the corresponding monomer (see Fig. 4d), while two independent QDs should\nnot be much off that of the corresponding single QD. One sentence was rewritten with a new clause to illustrate this point\nin the revised manuscript (Line 218-221, page 11): “Transient PL measurements (Fig. 4d) reveal a double-channel PL\ndecay dynamics for single diatomic molecule with a much increased average lifetime (40 ns, ensemble PL quantum yield\nas 68%) relative to the corresponding monomer (25 ns, ensemble PL quantum yield as 97%), implying unlikelihood of\nemissions from two independent QDs in a dimer.”\nTwo, the PL decay dynamics of single diatomic molecule show neither PL intensity dependence nor PL wavelength\ndependence, strongly against PL decay dynamics from two independent and size-different QDs in single diatomic\nmolecule. One sentence was modified in the revised manuscript to exhibit these results (Line 216-218, page 10-page 11):\n“The PL decay lifetime of single diatomic molecule remains nearly constant across different PL intensity fractions and\nat different PL emission wavelength (Supplementary Fig. 11), expected for dual-peak PL originated from two split\nelectron levels in thermo-equilibrium54-59.”\nThree, the control sample (i.e., double-QD dimers with neither resolvable bonding-antibonding coupling nor dual-peak\nPL) confirms that single dimer without quantum coupling would show nearly identical PL decay dynamics with the\ncorresponding monomer (Supplementary Fig. S13), contrast to single diatomic molecule with a similar size distribution\nof the original monomers. One sentence was modified in the revised manuscript to illustrate this difference (Line 221-\n223, page 11): “Conversely, the PL decay dynamics of single double-QD—determined as a dimer emitter by the two\nindicators—and its corresponding monomer are nearly identical (Supplementary Fig. S12), in accordance with two\nindependent QDs in a double-QD.”\nRegarding the relatively low PL quantum yield and double-channel PL decay dynamics with long lifetime, we could not\nfinger-point to a certain cause at the moment. Instead, we made two tentative suggestions in the revised manuscript (Line\n223-227, page 11): “Presumably, the relatively low PL quantum yield of a typical sample of diatomic molecules could be\ndue to the subpopulation of trimers (8%), given a purified trimer sample always with a very low PL quantum yield (<\n10%). In addition, possible defects in the epitaxially-attached neck area of diatomic molecules could cause delayed\nphotoluminescence with a somewhat reduced PL quantum yield and quasi-double channel PL decay32.”\nComment 6: For the text it is not clear if the dipole orientation measurements of Fig. 4f are at RT or at low temperature.\nResponse: Thank you for pointing out this mistake. During the revisions, we added a statement to clarify this issue\nfollowing the discussion about Fig. 4f (Line 247-248, page 12): “On the contrary, either PL or PL of a diatomic\n1 2\nmolecule is linearly polarized (see raw data in Supplementary Fig. 13) at room temperature”. In addition, the\nexperimental conditions have been explicitly stated in the revised manuscript.\nComment 7: The measured g(2) values are not in line with the explanation. going from 0.05 to 0.83 cannot be explained\nsimply by a transition from one to two independent emitters. There has to be coupling there.\nResponse: Thank you for your valuable suggestion. It is true that, according to theory, the g(2) value of ~0.83 (~0.66 in\naverage, see statistics in Supplementary Fig. 15) for the double-QD is significantly higher than the theoretical prediction\nof two independent QDs in a double-QD. Though it does exclude possibility of single quantum emitter in this case, we\ndon’t have a clear clue for this fact. In the revised manuscript, we offered some tentatively analysis for this (Line 285-\n294, page14): “On contrast, the g(2) contrast surges to a value as high as ~0.83 for an atypical double-QD (Fig. 5a,\nbottom) and an average of ~0.6 without counting the atypical ones (Supplementary Fig. 15), excluding dominant\ncontributions from biexciton emission in a single quantum emitter. Theoretically, within the strongly quantum confined\nsize regime (i.e., with strong nonradiative Auger recombination), the g(2) contrast of two independent QDs in a double-\nQD could be calculated as g(2) = (1 + QY /QY )/2 ≈ (1 + QY (1+ k /k))/2 under weak excitation35. Here, quantum\nXX X XX NR r\nyields of biexciton and single-exciton by exciting either QD in a double-QD dimer are respectively denoted as QY and\nXX\nQY , and k and k represent the rate constants of nonradiative and radiative decay of its single exciton, respectively.\nX NR r\nWith the typical values of QY and QY the calculated g(2) contrast is close to the average excluding atypical g(2) of the\nXX X,\ndouble-QD. The atypical g(2) could be a result of an excessively low single-exciton QY due to accelerated nonradiative\nX\ndecay by formation of a double-QD.”\nResponses to the comments from Reviewer 2:\nGeneral comments: In the manuscript entitled “Monodisperse quantum-dot dimers unlocking molecular states at room\ntemperature”, Lei and colleagues demonstrate a generalizable synthetic strategy to prepare dimers and higher order\nstructures of epitaxially fused colloidal quantum dot structures and present compelling evidence for electronic coupling\nof the QD states at room temperature. The authors develop QD fusion chemistry which is distinct from existing\napproaches and provides much improved control over the attachment facet and uniformity compared to the established\nsilica sphere templated synthesis method. The electron microscopy data presented supports their claim of highly uniform\nand controlled facet specific fusion. I believe this is a considerable synthetic advance for the fused QD field in terms of\nmaterial quality. In addition, the authors show comprehensive optical characterization of the fused quantum dots\ndemonstrating signatures of delocalized electronic states. Given the quality of the results and impact it will have synthetic\nnanomaterials chemistry and nanoscale optoelectronic communities, I believe it is suitable for publication in Nature\nCommunications.\nWith that said, I have some broad suggestions for improving this manuscript which should be addressed before\npublication.\nResponse: We are grateful for the reviewer’s encouragement. No actions needed here.\nComment 1: Throughout the manuscript the authors claim that all the bonds in the neck must form simultaneously to\nachieve epitaxial fusion. There is no evidence presented to support this claim. Further, there is considerable evidence in\nthe literature that epitaxial fusion can be achieved thorough a necking process (For Example: Science 2012, 336 (6084),\n1014–1018 and Science 2012, 336 (6077), 61–64). The authors should have a more nuanced discussion about the\nmechanism considering the above manuscripts (and many others on this topic) so that all possibilities are discussed, and\nreaders are not mislead by strong unsupported claims about the mechanism.\nResponse: Sorry for this careless misleading. We didn’t believe all hundreds of bonds were built simultaneously. The\nintended meaning of “simultaneous” was formation of all the bonds coherently in the lattice of the neck of a dimer, which\napparently caused confusion. During the revisions, we changed the phrase “simultaneous and precise construction of\nhundreds of chemical bonds” to “precise construction of hundreds of chemical bonds” throughout the entire manuscript\n(five different places).\nMechanism of the facet-selective attachment was discussed to a certain extent in the original submission. In the revised\nmanuscript, this was discussed further by incorporating the literature studies mentioned by the Reviewer (Line 153-158,\npage 8): “In comparison with a typically small (112̅0) facet of the original monomers43, the neck dimensions of homodimer\nincluding its thickness, width, and length (Figs. 3b-d) are excessively large. This suggests that the chemical bonds\nbetween two epitaxially-fused QDs should have followed the typical two-step oriented attachment studied by in-situ\nTEM49,50. In the first step, two QDs follow the site-selective coalescence at two of their relatively small (112̅0) facets\n(Supplementary Fig. 4) to form a facet-selective neck with a small cross section. In the second setp, the surface atoms\nwould move to the low-energy neck area through the known facet-reconstruction process in the given solvent system44.”\nComment 2: I worry about the yield of the process? Can the authors comment on the yield?\nResponse: In the original submission, yield of the dimer during synthesis was mentioned and the purity of the dimer\nfraction is given in Supplementary Fig. 2. In the revised manuscript, more details about yield were added (Line 95-100,\npage 5): “After 5-hour reaction under the given conditions, the conversion ratio from the nanoplatelet monomers to\nhomodimers for the optimized reactions can reach 50%-60%, and it is ~30% in average for all reactions studied.\nThrough\ntypical size-selective precipitation47, population of the homodimers can be consistently improved to 80~90%\n(Supplementary Fig. 2), with about 70~80% recovery ratio of the dimers in the specific fraction. The overall conversion\nratio of the nanoplatelets to homodimers through an optimized reaction/separation procedure can be as high as 35~45%.”\nComment 3: In Figure 3, the authors show structural characterization of dimers where they have varied the spacing of\nthe QD cores. From the figure, the description in the caption and main text it is not clear to readers how this was achieved.\nI infer that the authors synthesized nanocrystals with different shell thicknesses, then these were attached, resulting in\ndimers with different core-to-core spacing. However, this was not explicitly stated anywhere in the manuscript.\nResponse: Thank you for your valuable suggestion. Yes, the Reviewer was correct, that the CdSe@CdS dot@platelet\nnanocrystals were pre-synthesized through different reactions. Each type of homodimers were synthesized by oriented-\nattachment of a specific type of the pre-synthesized CdSe@CdS dot@platelet nanocrystals. This issue was clarified in\nthe revised manuscript (Line 162-167, page 8): “Experimentally, the CdS shells with a designated thickness are epitaxially\ngrown onto a given size (3 nm) CdSe core nanocrystals43. The resulting CdSe@CdS dot@platelet nanocrystals with three\ndifferent CdS shell thicknesses along the lateral direction (i.e., 2.5, 3.5, and 4.4 nm) are isolated, each of which is\ndissolved in octadecene at room temperature in the reaction flask. Subsequently, each reaction solution is heated up to\n280 oC under Ar atmosphere, into which the DoNH -OdNH entropic and dynamic ligands are introduced for the facet-\n2 2\nselective attachment (Fig. 2a).”\nComment 4: For the discussion on the interpreting the single particle PL and PL decay dynamics, the authors only\nconsider uncharged excitonic states and do not include charged states (Trions, etc.). Is this a good assumption? For\nsingle QDs, these charged electronic states are important for interpreting data such as blinking. The authors should\nprovide commentary to justify omitting the consideration of charged species in their analysis or they should consider\nthem in their analysis.\nResponse: Sorry for missing this part of information in the original submission. It’s true that there could be a sufficient\nnumber of dim states in some intensity trajectories of single “diatomic molecule”, which show emission properties\nexpected for the dim (trion) states. Importantly, steady-state spectrum, transient PL spectrum, polarization measurements,\nand bi-exciton measurements deposited in the main text are exclusively with the bright states. To clarify the concerns\npointed out by the Reviewer, we added experimental data for single “diatomic molecule” with a sufficient number of\ndime states as Supplementary Fig. 8, which demonstrates distinctive steady-state and transient PL spectra of both bright\nand dim states. In the main text, two sentences were added to clarify the steady-state and transient PL spectra in the main\ntext are exclusively from the bright-state (Line 193-196, page 9-page 10): “In some cases, single diatomic molecule can\nexhibit a PL intensity trajectory with a significant number of dim states generated by blinking, which offers a possible\nway to study optical properties of the dim states (Supplementary Fig. 8). The optical properties described below, including\nthose of single-exciton and bi-exciton, are for the bright state (or the neutral QD) unless otherwise specified.”\nDiscussion on distinction of the dual-peak emission of the bright states and emission of the dim states was added in the\nrevised manuscript (line 266-277, page 13): “Results in Supplementary Fig. 8 and Fig. 4c exclude possibility of the dim-\nstate emission (i.e., trion emission of singly-charged nanocrystal) as the high-energy PL in Fig. 4b (middle). Instead of\n2\na blue-shifted peak, the trion-state spectrum of single diatomic molecule shows a similar dual-peak PL with a minute\nred-shift of both peaks (Supplementary Fig. 8). In comparison with the bright-state emission, the PL /PL intensity ratio\n2 1\nof the dim-state emission of single diatomic molecule increases slightly due to increased thermal population of the\nantibonding orbital54-59. PL decay dynamics of the trion emission can be well fitted with mono-exponenital function with\na very short lifetime (~6.6 ns, Supplementary Fig. 8). Such a short lifetime is expected for the trion state from a QD with\nstrong nonradiative Auger recombination62, but the PL decay dynamics is starkly different from the bright-state PL. As\nmentioned above, the dual-peak PL in Fig. 4b (middle) is the bright-state emission of intensity trajectory for single\ndiatomic molecule, which shows no sign of contribution from this short-lifetime channel in the entire intensity range\n(Supplementary Fig. 11). In addition, it is difficult to imagine the intensity ratio between the dim- and bright-state\nemissions follows Boltzmann distribution in Fig. 4c.”\nComment 5: The QD molecules show lower QY compared to the monomers. I can’t help but wonder how the QY decrease\nof the dimers is manifested. Are all the QD molecules in the ensemble lower QY? The single particle PL and intensity\ntraces would suggest not as there is no off time and thus, they are high QY. Is it possible that the QD molecules which\nshowed the dislocations at the interfaces are completely dark? Not sure if the authors have the data to parse this, nor do\nthey need to give the current scope, but would be worth pointing out.\nResponse: Thank you for your valuable suggestion. At present, we could not finger-point to a certain cause for the\nrelatively low PL quantum yield. Instead, we made two tentative suggestions in the revised manuscript (Line 223-227,\npage 11): “Presumably, the relatively low PL quantum yield of a typical sample of diatomic molecules could be due to\nthe subpopulation of trimers (8%), given a purified trimer sample always with a very low PL quantum yield (< 10%). In\naddition, possible defects in the epitaxially-attached neck area of diatomic molecules could cause delayed\nphotoluminescence with a somewhat reduced PL quantum yield and quasi-double channel PL decay32.”\nComment 6: For fluence dependent TCSPC using the micro-liquid technique, authors should confirm that all\nmeasurements were done with appropriately low count rates for TCSPC to avoid artifacts in the decay traces and note\nthis in the methods section.\nResponse: Following the suggestion, the testing conditions and experimental details for fluence dependent TCSPC using\nthe micro-liquid technique have been thoroughly described in the methods section of the revised manuscript (line 411-\n415, page20): “Under a low repetition frequency (1 MHz), the nanocrystals in the micro-liquid freely diffusing in and out\nthe beam area would avoid interference of potentially charged nanocrystals during the saturation measurements.\nFurthermore, all micro-liquid measurements were performed with a low repetition frequency (1 MHz) to avoid artifacts\nin the decay traces recorded by TCSPC.”\nResponses to the comments from Reviewer 3:\nGeneral comments: The present manuscript reports interesting synthetic advances whereby colloidal CdS platelets\ncontaining nearly-monodisperse CdSe quantum dots (QDs) are attached laterally, so as to form dimers, trimers or\ntetramers. This is a potentially important step forward in the development of 'artificial molecules', built by tunnel-\ncoupling electrons confined in nearby quantum dots. I would be pleased to recommend publication of this work in Nature\nCommunications if the authors provide compelling evidence that the work is a significant advance with respect to\nprevious attempts of building artificial molecules out of core/shell CdSe/CdS quantum dots (Ref.31 and ensuing studies,\nsuch as Refs. 6,8,19,21,22,33-37). I list my specific concerns and suggestions below.\nResponse: We are grateful for the reviewer’s encouragement. Response to the specific comments are as follows.\nComments 1: Please make clear what is the morphological advantage of the present system as compared to that of\nRef.31 to produce dimers.\nResponse: Sorry for not being thorough on stating the advantage. We modified the last paragraph of the Introduction in\nthe revised manuscript to address this issue (line 153-158, page 8): “In comparison with a relatively small (112̅0) facet\nof the original nanoplatelet monomers31, the neck dimensions including its thickness, width, and length (Figs. 3b-d) are\nlarge. This suggests that the chemical bonds between two epitaxially-fused QDs should have followed a typical two-step\noriented attachment studied by in-situ TEM49,50. In the first step, two QDs follow the site-selective coalescence at two\nrelatively small (112̅0) facets to form a facet-selective neck with a small cross section (Supplementary Fig. 4). In the\nsecond step, the surface atoms would move to the low-energy neck area through the known facet-reconstruction process\nin the given solvent system44.”\nComment 1.1-The dimensions of the CdSe QDs and the QD-to-QD distances are similar here and in Ref.31, and so are\nthe absorption and PL redshifts at room temperature (up to 9 meV in Fig.3b, 13.5 meV in Ref.31).\nResponse: It’s true that, under low-resolution TEM, dimers presented here are quite similar to those reported by the\nBanin group. The key difference is the facet-selective epitaxial attachment that offers dimers with unique attachment\naxis, instead of randomly-oriented and often non-epitaxially attached in Ref. 31. According to theory as well\nexperimental results reported by the Banin group, epitaxial attachment is a must for formation of molecular bonding\nand antibonding states. While the red-shifts of absorption and PL are similar to each other for ensemble\nmeasurements, the PL decay dynamics of the diatomic molecules shows significantly elongated lifetime and PL\nquantum yields are much higher. In addition, the orthogonally-polarized dual-peak PL of single diatomic molecule\nwas not observed by the Banin group. Instead, they found two peaks of such dual-peak (or multi-peak) PL of a dimer\nwould possess either similar polarization angle or randomly-oriented transition dipole, consistent with two quantum-\nuncoupled QDs.\nThe key structural and electronic differences between our diatomic molecules and the homodimers reported in Ref. 31\nare discussed in detail in several parts of the revised manuscript. For instance, in the Introduction section of the revised\nmanuscript, one paragraph is added (Line 58-66, page 3): “However, despite extensive optimization of core spacing, neck\ndimension, and core size in the hetero-facet attached homodimers31,33,36, dual-peak PL of single homodimer observed\nusing single-molecule spectroscopy is inconsistent with those associated with molecular bonding and antibonding states.\nFor instance, at cryogenic temperatures, all detectable states of single CdSe/CdSe dimer are assigned to two uncoupled\nQDs34. Specifically, time-resolved single-molecule spectroscopy measurements confirm that multiple emission states are\neither the single-exciton emissions of two QDs with slightly different emission energy or combination of one neutral\nexciton and one trion state. Furthermore, two peaks of such dual-peak (or multi-peak) PL of a dimer would possess either\nsimilar polarization angle or randomly-oriented transition dipole, consistent with two quantum-uncoupled QDs10,34.”\nAnother example addressed the specific difference on polarization (Line 249-251, page 12): “The orthogonally-polarized\ndual-peak PL is distinctively different from a pair of emission peaks resolved at cryogenic temperatures of single hetero-\nfacet attached homodimer of two spheroidal CdSe/CdS core/shell QDs34, illustrating advantages of the facet-selective\nattachment disclosed here.”\nComment 1.2- Lines 36-38 state that artificial molecules with monodisperse geometric dimensions have not been\nreported before. Does this mean that the monodispersity of dot-in-platelets is higher than that of dot-in-dots? If so, please\ncompare data from the two systems. Ref.34 (cited in line 62) may not be very representative: it seems the authors\nintentionally chose heteronuclear QDs to simplify the analysis of trion location.\nResponse: Sorry for our unclear expression. For artificial molecules, monodisperse geometric dimensions mostly refer\nto their “molecular features”, instead of the QD monomers. Besides monodisperse size, shape, and crystal structure of\nQD monomers, monodisperse neck dimensions and crystallinity of artificial molecules are critic for formation of the\nmolecular bonding and antibonding states.\nTo clarify this issue, the related sentence is revised (Line 36-37, page 2): “However, synthesis of colloidal “artificial\nmolecules” with monodisperse geometric dimensions, especially the neck dimensions, neck epitaxy quality, and facet\nselectivity of the epitaxial attachment, has not been reported though extensive efforts have been devoted to this important\nfield since 1990s6,7,19-22.”\nComment 1.3- Perhaps the orientation of the piezoelectric field (c-axis) is different and matters?\nResponse: The piezoelectric field of the nanoplatelets might be different from that of the spheroidal ones, but we have\nnot observed much effects of it. Conversely, the electronic properties of the facet-selective homodimers are strongly\ndependent on the neck length, as predicted by the theory. Thus, we decided not to discuss piezoelectric field effects in\nthe revised manuscript.\nComments 2: The TEM-correlated single-molecular spectroscopy of Fig.4 is a very interesting probe for this system.\nHowever, I have concerns regarding the origin of the dual-peak PL.\nResponse: We are grateful for the reviewer’s encouragement. Regarding nature of the dual-peak PL, responses are\nprovided below.\nComment 2.1- The double peak may simply reflect emission from the left and right QDs, which are likely not identical.\nIn dimers, the non-radiative relaxation to the largest QD would induce a redshift as compared to monomers (where no\nsuch relaxation is possible), and it could be consistent with a Boltzmann thermal distribution. I would be more convinced\nif a systematic correlation of \"Delta E\" (the energy splitting between PL1 and PL2) was observed as a function of the\ndot-to-dot distance. The three instances of Ref.4b are insufficient.\nResponse: Thank for your value suggestions. Though we did not make it clear in the original submission, we did\nsystematically observe dot-dot distance dependence of the dual-peak PL. In the revised manuscript, we emphasized all\n(~50 in total for a specific sample) diatomic molecules (with 7.8 nm dot-dot core-spacing) show dual-peak PL with “Delta\nE” dictated intensity (Fig. 4c), while all double-QD nanocrystals (11.4 nm core-spacing) show single Lorentzian PL peak\n(Supplementary Fig. 9). During the revisions, details on this core-spacing dependence were added in several different\nplaces.\nLine 198-207, page 10 addresses the core-spacing dependence: “While the PL spectrum of single monomer shows single\nLorentzian peak (Fig. 4b, top), single diatomic molecule (core-spacing 7.4 nm) possesses dual-peak PL (Fig. 4b, middle),\nwhich is distinctly divergent from single yet broad PL peak exhibited by hetero-facet attached homodimers of CdSe/CdS\ncore/shell QDs31,33. Conversely, the PL spectrum of a double-QD (core-spacing 11.4 nm) is nearly identical in its contour\nand peak width with the corresponding monomer (Fig. 4b bottom). Statistically (Supplementary Fig. 10), all double-QD\nspectra can be well-fitted with single Lorentzian peak similar to that of single monomer (Fig. 4b top), consistent with two\nindependent QDs in a double-QD. Given the original monomers of two reactions with similar ensemble-PL peak width\n(Fig. 2b top and bottom), results of double-QD measurements—each with single Lorentzian peak—strongly suggest that\nthe commonly-observed dual-peak PL of single diatomic molecule should not be a result of emissions from its two\nindependent QDs.”\nLine 209-214, page 10 further states the statistic reproducibility of dual-peak PL of single diatomic molecule that satisfies\nthe thermo-population: “Experimentally, each diatomic molecule judged by the correlated TEM-spectroscopy\nmeasurements and/or the unified-intensity indicator (50~60 in total for a specific sample) shows the dual-peak PL. The\ndual-peak PL of single diatomic molecule can be deconvoluted into two peaks, i.e., PL and PL in Fig. 4b (middle).\nThe\n1 2\nsplitting energy between PL and PL (∆E) of ~50 diatomic molecules of the specific sample is 36.4±11.0 meV\n1 2\n(Supplementary Fig. 11). The intensity ratio between PL and PL of the diatomic molecules follows a Boltzmann\n1 2\ndistribution54 (Fig.4c), in accordance with single exciton emission from two split electron levels in thermo-equilibrium.55-\n59”\nComment 2.2-Also, Ref.46 shows dual-peak PL but it has no molecular coupling. Is that mechanism blocked here?\nResponse: Yes, the dual-peak PL reported in the literature (Ref. 46 in the original submission) is specifically ascribed\nto the weakly quantum-confined nanocrystals with a very small intraband gap. In this work, all QDs applied as in the\nstrongly quantum-confined size regime, whose intraband energy splitting in the conduction band is much greater than\n~35 meV Delta E observed here for the dual-peak PL, which would be hardly accessible for thermal population at room\ntemperature.\nComment 3: The interpretation provided in Fig.4e (and lines 184-186) seems speculative at this stage. An electron\ntunneling energy of few tens of meV cannot compete against exciton binding energies of few hundred meV. In CdSe/CdS\nQD molecules, it was shown that the latter traps the electron next to the hole, which is localized in the CdSe QD, thus\npreventing delocalization along the neck (see e.g. Chem. Mater. 2024, 36, 11676). Why is it different here?\nResponse: The dual-peak PL observed for diatomic molecules observed here as well as in the literature (MBE-grown\nones) at cryogenic temperatures (Science, 1997, 278, 1792.; Science, 2001, 291, 451.; Science, 2002, 297, 70.; Science,\n2006, 311, 637) are not delocalization of the electron wavefunction. Instead, it is a result of quantum coupling of two\nenergy levels in the two QDs of a diatomic molecule. Either with or without electrons filled in, formation of molecular\nbonding and antibonding orbitals—new orbitals exclusively for artificial molecules—is there, similar to formation of\nmolecular orbitals of H by overlapping of atomic orbitals of two hydrogen atoms. In the case of H , the electron and\n2 2\nnucleus interaction of an atom is excessively strong and would keep the electron tightly within the atomic orbital, but\nformation of H molecular orbitals always occurs as long as overlapping (coupling) of two atomic orbitals is in place.\nproperties are generally related to the periodic (Bloch) part of the wavefunction, rather than the envelope one (which is\nthat affected by molecular tunneling). Ref.52 is cited in the manuscript, but there the changes in polarization were a\nconsequence of suppressing the exciton fine structure (which involves the Bloch part of the wavefunction). Is the fine\nstructure playing a role here?\nResponse: Polarization-resolved micro-photoluminescence (μPL) spectroscopy revealed fine-structure splitting of\nexcitons in InAs/GaAs quantum dot molecules (Ref. 52). Previous studies demonstrated that the fine energy-level splitting\noriginates from interdot electronic coupling (Science, 2001, 291, 451.; Phys. Rev. Lett. 2003, 90, 086404.; Phys. Rev. B.\n2005, 71, 125335. etc.). These findings collectively establish that the observed energy-level splitting results from\ncoupling-induced electron state hybridization in these quantum-dot molecules.\nComment 5- Similar to point 3, the interpretation of biexciton (BX) emission in Figs.5e-g misses the influence of\nCoulomb interactions. Not only is electron-hole attraction expected to drag electrons into the CdSe QD, but also hole-\nhole repulsions are expected to make the configuration of Fig.5g very energetic. Its emission should appear blueshifted\nwith respect to that of Fig.5f. Yet, Fig.5d shows no shift of BX with respect to X. Can the authors estimate biexciton\nbinding energies for different emission channels?\nWhy does the BX behave differently from that of Ref.37, where the two BX decay channels were simply associated to one\nX in each QD, or two X in the same QD?\nResponse: Thank you for reminding us to estimate the binding energies of biexcitons. Yes, one type of the bi-excitons\n(cBX) should possess significant biexciton bonding energy (~35 meV according to theory), but its hole nonradiative\nAuger recombination is strong that it contributes little to the PL spectra. Bonding energy of the other type of the bi-\nexcitons (sBX) was theoretically estimated to be zero, given two holes completely separated from each other and two\nelectrons delocalized in the molecular orbitals. This unique electron and hole configuration also implies nearly identical\nPL spectrum with the single-exciton. During the revisions, a paragraph was added (Line 327-334, page 16): “According\nto Figs. 5b-c, contributions to the total PL from the molecular biexciton cBX and sBX are negligible and ≤ 10%,\nrespectively, within the excitation power range. The wavefunction configuration of the long-lifetime molecular biexciton\n(sBX, Fig. 5f) is almost the same as that of either single-exciton (Fig. 5e) or the corresponding trion. Thus, the steady-\nstate PL spectra at the ensemble level should be insensitive to the excitation intensity in Fig. 5d. This conclusion is also\nconsistent with theoretic calculations37, which predicted that biexciton binding energies of the sBX and cBX biexciton\nstates of homodimers with similar dimensions should be ~0 meV and ~35 meV, respectively.”\nThe key difference on biexciton behaviors from that reported in Ref. 37 (original submission) is the homodimers with\nthe shortest core-spacing (7.4 nm) are found to form molecular bonding and antibonding orbitals, instead of two\nindependent QDs in a double-QD nanocrystal. In fact, both cBX and sBX states—especially the latter—is largely affected\nby the molecular orbitals.\nComments 6- More technical comments:\nComment 6.1- What is the temperature in the single-molecule spectra of Fig.4? If it is room temperature, why is the\nBoltzmann distribution not giving a ratio of 1 for energy splittings of 24 meV (thermal equilibrium is claimed in line 174)?\nResponse: The single-molecule spectra in Fig. 4 were measured at room temperature, which is clarified in the revised\nmanuscript (Line 167-168, page 8): “All spectroscopy measurements below are carried out at room temperature.”\nThe intensity ratio between PL and PL of the diatomic molecules follows a Boltzmann distribution, I /I = e-E/kT. If\n1 2 PL2 PL1\nthe splitting energy E is 24 meV, almost the same as the thermal energy kT at room temperature, the intensity ratio of\nPL to PL I /I would be ~1/e = 0.37, which is significantly smaller than one.\n2 1 PL2 PL1\nComment 6.2- Can the lifetime of PL1 and PL2 be disentangled? If molecular effects play a role, the radiative decay of\nPL2 should be longer lived than that of PL2 (because bonding orbitals have more charge in the barrier).\nResponse: Yes, we tried to disentangle the two channels. However, the PL decay dynamics of the diatomic molecules\nshow neither wavelength or intensity dependence (Supplementary Fig. 11). This thought to be reasonable, given the rapid\nthermal mixing of two molecular states. One sentence is modified in the revised manuscript to address this concern (Line\n216-218, page 10-page 11): “The PL decay lifetime of single diatomic molecule remains nearly constant across different\nPL intensity fractions and at different PL emission wavelengths (Supplementary Fig. 11), expected for dual-peak PL\noriginated from two split electron levels in thermo-equilibrium.”\nWe thank the reviewers for their valuable comments and suggestions.\nRESPONSE TO REVIEWERS\nof “Monodisperse quantum-dot dimers unlocking molecular states at room temperature” by Hairui Lei,\nHaiyan Qin, Haixin Lei, Yuqing Wang, Jiongzhao Li, Xiaogang Peng\nResponses to the comments from reviewer #1:\nGeneral comments: Overall, it is clear that the authors have made a significant effort to address referee comments. I\nhave to say that despite this I am not completely convinced that the origin of the reported results is the presence of an\nanti-bonding orbital and not, specifically, size disparity within the dimer. The strongest proof for that is the polarization\norientation. The single Lorentzian peak emission of single double-QD can be due to the reduced disparity between the\npair of emitting dots under these conditions and the increased lifetime could still be due to reduced overlap of the electron-\nhole pair upon increase of the volume of the nanocrystal. Yet, the results by themselves can be sufficient for publication.\nSometimes it is best to leave the reader with a somewhat open question. As such, I would recommend publication of the\nmanuscript while still urging the authors to consider the following.\nResponse: Thanks for your appreciation of our efforts, especially the synthesis. We recognized the hesitation in affirming\nthe assignments of molecular bonding and antibonding states, and decided to tune the focus during the revisions.\nWithout emphasizing affirmation of molecular states, drastic advancements on synthetic chemistry remains as the main\ncontent (related to Fig. 1-3). For the unique yet reproducible optical properties (related to Fig 4-5), we simply describe\nthem and points out that they are expected for the molecular states. This somewhat shift of focus is reflected by title\nof the manuscript, which is revised to “Unidirectionally epitaxy-attached quantum-dot dimers with unique optical\nproperties”. Also, the last two subtitles in Results section are changed as follows: “Single-molecular\nspectroscopy of single <11𝟐̅ > -attached homodimer” and “Biexciton properties of the <11𝟐̅ > -\nattached homodimers”. In the Abstract and main text, all statements on assignment of molecular states are\nremoved, which are replaced by stating facts and comparing results with theories.\nComment 1: It is crucial that the authors address the issue of the\nappearance of bonding and anti-bonding states when the two dots are\nreally nondegenerate (actually Figure 1b exemplifies that the dimers are\nactually quite heterogeneous...)\nResponse: As stated above, this revision would mostly stick to synthetic\ndevelopment, and the unique optical properties remain as stating facts.\nIn addition to existing data (e.g., steady-state and transient PL spectra of\ndouble-QDs), more results in Supplementary Fig. 10 (also see Figure to\nthe right) are provided to disconnect the dual-peak PL with size distribution of the QD monomers (Page 13, Line 265-\n275, revised manuscript with marks): “Fig. 1 shows that the lateral dimensions of CdSe@CdS dot@nanoplatelets are\nsomewhat broad, which is known to affect optical uniformity less than their better-controlled thickness43. In addition, the\nsingle Lorentzian peak emission of single double-QD (Supplementary Fig. 9), the polarization measurements in Fig. 4b\n(inset, top plot) and Fig. 4f, the much increased PL decay lifetime (Fig. 4d), and the Boltzmann distribution of peak areas\nof the two peaks based 50-60 dimers (Fig. 4c) all suggest that the dual-peak PL would be unlikely from two independent\nQDs in a dimer. Statistic results for ~50 single QD and ~50 early-termed single diatomic molecule are summarized in\nSupplementary Fig. 10. The Statistic results illustrate that the average energy position of PL peak of single QD is between\nthose of the two peaks of dual-peak PL, and distribution profile of the high-energy (or low-energy) peak for dual-peak\nPL extends significantly beyond the low-energy (or high-energy) end of single QD, respectively. These results are against\neither simple size variation or Förster resonance energy transfer arising from size dispersity of two QDs in a homodimer\nwith the smallest core-spacing in Fig. 3a.”\nComment 2: The modifications to the section on BX made it a lot less clear. Also - the discussion suddenly shifted from\nmolecular orbitals to a language of \"segregated\" and \"confined\" biexcitons, which is very counterintuitive. How do these\ntwo pictures work together?\nResponse: Sorry for not being clear. We revised the biexciton section significantly, with the subtitle changed to\n“Biexciton properties of the <11𝟐̅> -attached homodimers” to avoid any strong claim about the molecular\nstates. In the last submission, we did not make it clear that discussion on \"segregated\" and \"confined\" biexcitons is\nstill in the context of molecular orbitals. During the revisions, despite of not affirming molecular biexcitons, the starting\npart of this section is rewritten (Page 15, Line 324-333, revised manuscript with marks): “All results about biexcitons for\nthe homodimers with the smallest core-spacing can be interpreted using the band-edge energy diagram of diatomic\nmolecule in Fig. 4e, which leads to a simplified scheme for its band-edge single-exciton in Fig. 5e, i.e., with the electron\nin either bonding or antibonding state and the hole in one of two uncoupled core states. In this molecular diagram, there\nwould be two types of distinguishable biexcitons in a diatomic molecule. If two holes are separately localized on two\nepitaxially-attached core QDs in a diatomic molecule (Fig. 5f), there would be only one effective Auger nonradiative\nrecombination channel. Specifically, one spatially-delocalized electron in either bonding or antibonding orbital and one\nlocalized hole recombine and pass the energy to the other spatially-delocalized electron. Given the bonding and\nantibonding electron states being delocalized in both QDs in a homodimer, this would result in suppression of the Auger\nnonradiative recombination in comparison with that in the corresponding monomer.”\nComment 3: It is good that the authors added references 38, 40 and 41, but what do references 39 and 42 have to do\nwith dual emission or the presence of two potential minima?\nResponse: Sorry for the careless citations. Reference 39 should be the paper published by the same group of authors in\nJACS (Battaglia et. Al., Coupled and Decoupled Dual Quantum Systems in One Semiconductor Nanocrystal, J. Am.\nChem. Soc., 2>>5, 127, 10889-10897.). Reference 42 should be another paper on a similar system (Oron et. al.,\nLuminescence upconversion in colloidal double quantum dots, Nat. Nanotech., 2013, 8, 649-653.). During the revisions,\ntwo old references are replaced by two correct ones.\nResponses to the comments from reviewer #2:\nGeneral comments: The authors have addressed my technical concerns. I believe the results are of sufficient novelty\nand quality for the broad readership audience of Nature Communications. I believe the manuscript is now suitable for\npublication in Nature communications.\nResponse: We are grateful for the reviewer’s encouragement. No actions needed here.\nResponses to the comments from reviewer #3：\nGeneral comments: After reading the revised manuscript and the authors response letter, my impression is similar to\nthe initial one. This is an exciting work, a step forward in the attempt to develop colloidal quantum dot\nmolecules, and it contains intriguing results (dual PL with different polarization). However, the text contains strong claims about the\nachievement of quantum coupling which, at present, are not sufficiently solid.\nThe revised manuscript has improved the introduction by better comparing with earlier works, and there are new relevant\ndata to discard alternative interpretations of the experiments (Supp. Figures 8 and 9). However, little effort is made to\nprove their interpretation (quantum coupling) right. To be specific: (a) there are no systematics proving the splitting\nbetween PL and PL behaves as one expects from quantum tunneling; (b) there is no explanation of why the magnitude\n1 2\nof the splitting between PL and PL in diatomic molecules with 7.8nm dot-to-dot core spacing is much larger than in\n1 2\ntheoretical predictions of related systems, (c) the different polarization of PL and PL is tentatively ascribed to the fine\n1 2\nstructure, but there is no explanation of why bonding and antibonding orbitals should have different opposite fine\nstructure.\nResponse: Thanks for your appreciation of our work. We carefully thought about your comments during this run of\nrevisions, and agreed that those strong claims about quantum coupling were without sufficiently solid ground. It is true\nthat the main achievements of this work should be the breakthrough on colloidal synthesis of single-crystalline\nhomodimers with unique epitaxial attachment and observation of some interesting optical properties from those with the\nclosest core-spacing. Though these interesting optical properties are consistent with expectation of quantum-coupled\ndiatomic molecules, it would take a series of efforts to eventually affirm the claims.\nWith these thoughts, we decided to somewhat shift the focus of this submission. The new synthetic approach and the\nresulting well-controlled homodimers remain as it is (related to Fig. 1-3), and discussion on unique optical properties\n(related to Fig 4-5) shifts from strong claims on quantum coupling to stating the facts and the consistency with theoretical\nexpectations. Such consistency is further enhanced by additional experimental results that help to exclude other\npossibilities (such as size distribution of the QD monomers).\nThe shift of focus is also reflected by a new title should be better suited for the revised manuscript, which is now as\n“Unidirectionally epitaxy-attached quantum-dot dimers with unique optical properties”.\nComment 1.1: In my previous report (Comment 2.1) I asked for evidence of correlation between core-to-core\ndistance and PL -PL splitting. The authors respond that all (~50) diatomic molecules show dualpeak PL, but do not show a\n1 2\nsystematic comparison of distance vs splitting. In Supplementary Fig.10 they show considerable dispersion for the\nsplitting (from 30 to 70 meV), and in Fig.3 of the main text they show dispersion in the core-to-core distance (from 6.0 to\n10.0 nm). A plot showing that the splitting increases exponentially as the core-to-core distance decreases would be a\nstrong indication of tunneling.\nResponse: Thank you for your valuable suggestion. We would love to show the energy splitting and the core-spacing.\nUnfortunately, dual-peak PL is only observable for single homodimer with the smallest core-spacing (7.8 nm), single\nhomodimer PL with 11.4 nm core-spacing in Fig. 3 is always single peak (see Fig. 4b), and the other sample does not\noffer reliable measurements at room temperature. This means that cross-sample correlation would not be possible. For\nthe homodimers with 7.8 nm average core-spacing, it was very difficult to reach a needed spatial resolution under TEM-\noptical correlated measurements for establishing a plot to show an exponential increase of energy splitting upon\ndecreasing the core-spacing. Experimentally, CdSe core size and CdS shell thickness for the QD monomer for\nsynthesizing the homodimers with the smallest core-spacing are 3.2 nm and ~7 monolayers of CdS shells, respectively.\nAt present, synthetic control is insufficient to either further reduce the shell thickness or precisely tune the shell thickness\nof CdSe@CdS dot@nanoplatelets. Specifically, further reduced CdS shell thickness would hardly retain the nanoplatelet\nshape of the core/shell QDs. At present, thickness control of the core/shell QDs would be within 1~2 monolayers,\ncorresponding to 3~4 monolayers of the CdS shells between two cores in a homodimer. This means that, at present, it\nwould be prohibitive to establish the core-spacing and energy-splitting correlation reliably. As synthetic chemistry of the\nQD monomers and shell epitaxy advances in the future, we expect this important relationship would become available.\nTo address this issue from a different angle, we provide statistical data for distributions of the single PL peak for QD\nmonomer, PL and PL of dual-peak PL of single homodimer with the\n1 2\nsmallest core-spacing (7.8 nm), which are shown in Supplementary Fig.\n10c in the revised manuscript (also see Figure to the right). Figure to the\nright reveals that, while three distributions show similar distribution in\nenergy, average PL (1.999±0.018 eV) and PL (2.036±0.021 eV)\n1 2\npeaks of single homodimer with the smallest core-spacing (7.8 nm)\nrespectively exhibit blue-shift and red-shift relative to the monomer's PL\npeak (2.014±0.020 eV), while the PL spectrum of single double-QD\n(the core spacing is 11.4 nm) shows single Lorentzian peak. The results\nare also described in the revised manuscript (Page 10, Line 217-220):\n“Statistical results reveal that, relative to the corresponding monomer's PL peak at 2.014±0.020 eV, PL and PL exhibit\n1 2\nblue-shift to 1.999±0.018 eV and red-shift to 2.036±0.021 eV, respectively (Supplementary Fig. 10). These results are in\nagreement with the electron bonding and antibonding energy level splitting caused by quantum coupling between two\nQDs in a homodimer.” and in Line 270-275, Page 13: “Statistic results for ~50 single QD and ~50 early-termed single\ndiatomic molecule are summarized in Supplementary Fig. 10. The Statistic results illustrate that the average energy\nposition of PL peak of single QD is between those of the two peaks of dual-peak PL, and distribution profile of the high-\nenergy (or low-energy) peak for dual-peak PL extends significantly beyond the low-energy (or high-energy) end of single\nQD, respectively. These results are against either simple size variation or Förster resonance energy transfer arising from\nsize dispersity of two QDs in a homodimer with the smallest core-spacing in Fig. 3a.”\nFurthermore, we removed strong claims that assigned the dual-peak PL to the molecular states. Instead, we simply state\nthe dual-peak PL is consistent with the theoretical expectations of diatomic molecules. For instance, Page 11, Line 235-\n237: “Results in Fig. 3b and Figs. 4a-c all suggest that quantum coupling of the band-edge electron atomic orbitals (1S(e))\nlikely exists between two QDs in a homodimer with a small (7.8 nm) core-spacing (see Fig. 3a), which forms the band-\nedge bonding and antibonding electron orbitals (or molecular states)5,6,19-22,42,52”, and Page 11, Line 239-242: “The\naverage splitting energy ∆E (~35 meV) between PL and PL is in the same magnitude of the bonding-antibonding\n1 2\nsplitting energy predicted for diatomic molecules with similar dimensions in the literature19, though the exact value of\nenergy splitting between bonding and antibonding electron orbitals is under debate42.”\nComment 1.2: Related to this point: the authors say all double QDs with mean core-to-core distance of 7.8nm show\ndual-peak PL, while none of those with mean core-to-core distance of 11.4 do so. However, the histogram distribution in\nFig.3 shows that the former contain a few instances with distance ~10 nm, while the latter contain a few instances with\ndistances down to 9 nm. What is the difference, then?\nResponse: There are two experimental reasons for the inconsistency pointed out by the Reviewer. Firstly, as mentioned\nabove, the TEM measurements could hardly distinguish the core-spacing difference within ~1 nm. In addition, size\ndistribution of the core/shell QD monomers is also in this range. Secondly, size distribution histograms of homodimers\nin Fig. 3a are based on approximately 300 particles, while single-particle spectroscopy measurements are conducted on\n30~60 particles and could readily miss a tiny fraction of odd homodimers.\nTo address this issue, two sentences are modified in the revised manuscript. Page 10, Line 211-213: “Within the statistical\nerror, each homodimer with the smallest core-spacing (7.8 nm) judged by the correlated TEM-spectroscopy\nmeasurements and/or the unified-intensity indicator (50~60 in total for a specific sample) shows the dual-peak PL, each\nof which can be deconvoluted into two peaks, i.e., PL and PL in Fig. 4b (middle)” and Page 10, Line 204-206: “Within\n1 2\nstatistical error (Supplementary Fig. 9), all double-QD spectra can be well-fitted with single Lorentzian peak, similar to\nthat of single monomer, consistent with two independent QDs in a double-QD.”\nComment 1.3: Minor issue: Fig.4b is a bit misleading. It shows monomers and double QDs with nearly identical\nemission (center at ~2.0 eV), and a diatomic molecule with PL1 at 2.0 eV and PL2 at ~2.05 eV. If tunneling was acting,\nPL1 and PL2 should be red and blue shifted around 2.0 eV, respectively. After seeing Supp. Fig.9, I understand that the\nmonomers have some dispersion (emitting few tens of meV above or below, not that different from the splitting between\nPL1 and PL2), so Fig.3 is just a convenient selection.\nResponse: Thank you for your understanding and pointing out this\ninteresting fact. This prompted us to statistically analyzed the single-\nparticle PL peak energies for single homodimers with the smallest core-\nspacing and the corresponding single QD monomer. Results in\nSupplementary Fig. 10c (also the Figure to the right). As expected,\nsingle-peak PL of single QD monomer is indeed between PL and PL\n1 2\npeaks of dual-peak PL.\nDiscussion and revisions about the new results in the Figure to the right\nare provided above.\nComment 2.1: This is again related to comment 3 of my previous report, and to comment 4 of Referee 1. The authors\nresponse to these points is not convincing. In Fig.4e and Fig.5e-g (as well as the discussion in the text), the authors show\nbonding and antibonding electron states, whose splitting they claim to be responsible for the PL1-PL2 splitting (20-70\nmeV). The magnitude of this splitting is way larger than theoretical estimates for CdSe/CdS dimers, and no explanation\nis given for it. The authors say that the energy splitting is consistent with J. Chem.\nPhys. 2022, 157, 134502: «Theoretical calculations in Ref.21 predict that (0001)\nand (10-10) facet-connected CdSe/CdS core/shell homodimers (2.8 core diameter, 7\nnm total diameter, 5 nm neck width) exhibit bonding and antibonding orbital\nsplitting energies of ~25 meV and ~15 meV». Lacking more information, I guess these\nnumbers are taken from the green symbols in Fig.4a of that paper:\nHowever, the figure does not represent the bonding-antibonding splitting, but the\nexcitonic gap redshift upon formation of a dimer, where several factors contribute\n(including relaxed confinement, which is responsible for 80% of the shift).\nResponse: Sorry for not being clear. As mentioned above, this reversion of manuscript shall not claim affirmation of\nbonding and antibonding splitting for the unidirectionally epitaxy-attached homodimers. Instead, we would state the facts\nand, in the appropriate places, compare the optical properties with theory. As for the energy splitting between PL and\n2\ncalculations, such as that reported in Ref. 21 (J. Chem.\nPhys. 2022, 157, 134502). Yes, Fig.4a in Ref. 21 quoted\nby the Reviewer does not represent the bonding-antibonding splitting in their calculations, but Fig.2 (also\nsee Figure to the right) offers bonding and antibonding\norbital splitting energies of ~25 meV and ~15 meV for\nCdSe/CdS core/shell homodimers with similar\ndimensions reported here (2.8 core diameter, 7 nm total\ndiameter, 5 nm neck width). Specifically, these numbers\nare taken from the green symbols in Fig.2 (right panel) of\nthe reference and marked in the Figure to the right, and\nthe red lines and arrows provide a guide to observe the\ntunneling splitting energy.\nHowever, we do agree that these calculated values are for\nCdSe/CdS core/shell homodimers with different attached-\nfacets. Instead of the (112̅0) facet-attached homodimers\nfocused here, the calculations in Ref. 21 are for the\nhomodimers with either (101̅0) or (0001) facet-attached. In addition, a recent theoretical paper published in Chem. Mater.\nhighlights that the coupling energy is associated with electron configurations of an excited states.\nWith these thoughts in mind, we decide to revise the related sentences in the text (Page11, Line 239-244) to only point\nout that the energy splitting between PL and PL is in the same magnitude calculated for the bonding-antibonding : “The\n1 2\naverage splitting energy ∆E (~35 meV) between PL and PL is in the same magnitude of the bonding-antibonding\n1 2\nsplitting energy predicted for diatomic molecules with similar dimensions in the literature19, though the exact value of\nenergy splitting between bonding and antibonding electron orbitals is under debate42. It should be noted that the\nhomodimers discussed in this subsection are all epitaxially-attached along the <112̅0> axis that is different from those\noften considered in the literature6,19-22.”.\nComment 2.2: The secondary role of tunneling in excitons in Ref.21 brings us back to comment 3 of my first report. The\nelectron tunneling energy in CdSe/CdS dimers -which has been calculated to be of few tens of meV- decreases in the\npresence of a hole. This is because the hole (being heavy) does not tunnel, and it binds the electron near it through\nCoulomb attraction (few hundreds of meV, much greater than tunneling energy). A first hint of this can be found in\nFig.1g,h of Ref.31. Single electron calculations show 23 meV splitting between bonding and antibonding orbitals (1g),\nbut in the presence of Coulomb interaction with the hole (1h), all you have is electron localized either in one dot or in\nthe other, with little tunneling (60 meV splitting is the difference in energy between direct and indirect exciton, not the\ntunneling).\nThe same is observed in Chem. Mater 2024, 36, 11676, where the single-electron tunneling is significant，\nbut the excitonic one is strongly quenched (fraction of meV). Also for BX, the splitting is largely suppressed, and\namounts to few meV in a best case scenario (quasi-rod-like CdS shell).\nThese results challenge the current interpretation of the results in Figs.4-5 of the manuscript, so they should be\naddressed. Perhaps some modeling could show dot-in-platelets behave differently, but I am not sure why.\nAs for the authors response: the comparison with H2 molecule is not convincing. Surely, the protonelectron\nattraction is very strong, but so is the electron confinement energy (the Bohr radius of the 1S orbital is 0.5 Angstrom).\nThat is why delocalizing between 2 H nuclei is energetically favorable. In CdSe/CdS dimers the scale of both confinement\nand Coulomb energies is much smaller. The problem is that the low conduction band offset in CdSe/CdS, which is\nnecessary for the tunneling, is spoiled in the presence of a localized hole, which creates a deep potential well inside CdSe.\nResponse: Thanks for offering great insights on this critical issue. In the future, we might be able to develop a\ntheoretical framework to understand the CdSe@CdS dot@nanoplatelet homodimers by collaborating with theorists. For the\ncurrent submission, we would remove all strong claims on quantum coupling and only state facts and comparison with\ntheoretical calculations deposited in the literature. In addition to the revisions mentioned above, one more sentence is\nadded in the revised manuscript (Page12, Line 244-246): “In addition, all calculations in the literature were based on spherical\nCdSe/CdS core/shell QDs, the coupling energy of which may differ from that for homodimers of CdSe@CdS\ndot@nanoplatelet QDs.”\nComment 3: The different polarization of PL1 and PL2 as compared to monomers is tentatively ascribed to quantum\ncoupling, and Ref.60 is cited to this end. In Ref.60, the polarization is interpretated from the fine structure splitting bright\nexcitons (Bloch part of the wave function, in the language of my first report). The splitting between X and Y exciton\ndoublets is of micro-eV. In CdSe/CdS nanocrystals the splitting is somewhat larger (up to 3 meV, see e.g. ACS Nano 2012,\n6, 1979), but it is one order of magnitude smaller than the 20-70 meV splitting PL1 and PL2. It doesn’t match.\nAlso, why should bonding and antibonding orbitals have different fine structure?\nA more detailed, ad-hoc interpretation is needed.\nResponse: Thanks for pointing out this issue. At present, it would not be possible for us to offer a theoretical\ninterpretation of the origin of the orthogonally-polarized emission of the two peaks (PL and PL ). The paragraph is\n1 2\nsimplified to simply state the facts, and the mechanistic discussion only mentions exclusion of emissions from two\nuncoupled QDs in a dimer in the revisions (Page12, Line 252-260): “With its <0001> axis perpendicular to the substrate,\nPL intensity of single monomer remains unchanged upon rotating the polarization angle of detection (inset, Fig. 4b top),\nconsistent with a two-dimensional dipole on a plane parallel to the basal planes of a CdSe@CdS dot@nanoplatelet43.\nOn the contrary, either PL or PL of a diatomic molecule is linearly polarized (see raw data in Supplementary Fig. 13) at\n1 2\nroom temperature, with their transition dipoles perpendicular to each other (Fig. 4f). The orthogonally-polarized dual-\npeak PL is distinctively different from a pair of emission peaks resolved at cryogenic temperatures of single hetero-\nfacet attached homodimer of two spheroidal CdSe/CdS core/shell QDs34. Although the mechanism of orthogonally-polarized\ndual-peak PL is unclear, it at least suggests that the two PL peaks are very unlikely from emissions of two uncoupled\nQDs in a dimer, provided the distinctive polarization of a monomer (inset, Figure 4b top).”\nWe thank the reviewers for their valuable comments and suggestions.\nRESPONSE TO REVIEWERS\nof “Unidirectionally epitaxy-attached quantum-dot dimers with unique optical properties” by Hairui Lei,\nHaiyan Qin, Haixin Lei, Yuqing Wang, Jiongzhao Li, Xiaogang Peng\nResponses to reviewer #1:\nGeneral comments: I cannot say that I agree with the statement of the authors that the bonding-antibonding theme is a\nlot less accentuated in the present manuscript. In any case, as I have little more scientific input to add, I leave this at the\nhands of the editor.\nResponse: Thanks for the reviewer’s valuable comments and suggestions throughout the revision and evaluation process\nof the manuscript. No actions needed here.\nResponses to reviewer #3:\nGeneral comments: The revised version of the manuscript keeps the relevant findings in this work (synthesis approach,\npuzzling spectroscopy of dimers) while avoiding several claims in the interpretation which were insufficiently backed by\nthe data or models. I recommend publication of this (interesting) work as is.\nResponse: We are grateful for the reviewer’s encouragement. No actions needed here.\nWe thank the reviewers for their valuable comments and suggestions."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I cannot say that I agree with the statement of the authors that the bonding-antibonding theme is a lot less accentuated in the present manuscript. In any case, as I have little more scientific input to add, I leave this at the hands of the editor.", "reviewer_3": "Please see attached report."}, "author_response": "RESPONSE TO REVIEWERS\nof “Unidirectionally epitaxy-attached quantum-dot dimers with unique optical properties” by Hairui Lei,\nHaiyan Qin, Haixin Lei, Yuqing Wang, Jiongzhao Li, Xiaogang Peng\nResponses to reviewer #1:\nGeneral comments: I cannot say that I agree with the statement of the authors that the bonding-antibonding theme is a\nlot less accentuated in the present manuscript. In any case, as I have little more scientific input to add, I leave this at the\nhands of the editor.\nResponse: Thanks for the reviewer’s valuable comments and suggestions throughout the revision and evaluation process\nof the manuscript. No actions needed here.\nResponses to reviewer #3:\nGeneral comments: The revised version of the manuscript keeps the relevant findings in this work (synthesis approach,\npuzzling spectroscopy of dimers) while avoiding several claims in the interpretation which were insufficiently backed by\nthe data or models. I recommend publication of this (interesting) work as is.\nResponse: We are grateful for the reviewer’s encouragement. No actions needed here.\nWe thank the reviewers for their valuable comments and suggestions."}, {"round": 3, "reviewer_comments": {"reviewer_1": "I cannot say that I agree with the statement of the authors that the bonding-antibonding theme is a lot less accentuated in the present manuscript. In any case, as I have little more scientific input to add, I leave this at the hands of the editor.", "reviewer_3": "The revised version of the manuscript keeps the relevant findings in this work (synthesys approach, puzzling spectroscopy of dimers) while avoiding several claims in the interpretation which were insufficiently backed by the data or models. I recommend publication of this (interesting) work as is."}, "author_response": ""}]

Decision letter