Room-temperature quantum interference in single perovskite quantum dot junctions

The studies of quantum interference effects through bulk perovskite materials at the Ångstrom scale still remain as a major challenge. Herein, we provide the observation of room-temperature quantum interference effects in metal halide perovskite quantum dots (QDs) using the mechanically controllable break junction technique. Single-QD conductance measurements reveal that there are multiple conductance peaks for the CH3NH3PbBr3 and CH3NH3PbBr2.15Cl0.85 QDs, whose displacement distributions match the lattice constant of QDs, suggesting that the gold electrodes slide through different lattice sites of the QD via Au-halogen coupling. We also observe a distinct conductance ‘jump’ at the end of the sliding process, which is further evidence that quantum interference effects dominate charge transport in these single-QD junctions. This conductance ‘jump’ is also confirmed by our theoretical calculations utilizing density functional theory combined with quantum transport theory. Our measurements and theory create a pathway to exploit quantum interference effects in quantum-controlled perovskite materials.

Indeed, we cannot rule out the possibility that the gold electrodes can also slide along the 'diagonal' directions (shown as red arrows in Fig. 1). However, taking the 2x3x3 18Pb MAPbBr3 as an example, the gold electrodes only have 2 possibilities that slide along the 'diagonal' directions, while the 'horizontal' directions would be 10 possibilities, which is five times more than the former. Therefore, the gold electrodes have more chance to slide along the 'horizontal' directions. In addition, we also analyze the energies of sliding along these two directions. The corresponding total energies upon sliding along one unit cell are shown in Fig. S30c. Compared with displacement along the green 'horizontal' direction, the energy barrier is much higher in the red 'diagonal' direction, due to the existence of CH3NH3 + in the cavity. In addition, the distance between two adjacent Br atoms along 'diagonal' direction (around 0.8 nm) is much larger than the experimental value (the plateau length difference is about 0.5 nm see Fig. 3c in manuscript). This demonstrates that there is a low-energy channel for sliding along the 'horizontal' direction, whereas the 'diagonal' direction contains a high-energy barrier and is less likely to happen in a real experiment.
To enhance our understanding of the experiment, we added Fig. S30 to Supplementary Information (SI) and the following sentences to the manuscript: "After the rupture of the gold wire, the initial gap width is known to be a snap-back distance of about 5 Å. Since this corresponds to the distance between two neighbouring Br atoms (around 5 Å), these two Br atoms are most likely to be connected to the gold atoms at the beginning in this pulling process. As for the sliding direction, the gold electrode could slide from the top of one Br atom to its adjacent Br atom along the horizontal and diagonal directions (shown as green and red arrows in Fig. S30). The corresponding total energies upon sliding along one unit cell are shown in Fig. S30c.
Compared with displacement along the green 'horizontal' direction, the energy barrier is much higher in the red 'diagonal' direction due to the existence of CH3NH3 + in the cavity. This demonstrates that there is a low-energy channel for sliding along the 'horizontal' direction, whereas the 'diagonal' direction contains a high-energy barrier and is less likely to happen in a real experiment…... Therefore, the sliding along the 'horizontal' direction is adopted here to understand what we observed experimentally." Top view. The gold electrode is not displayed for clarity. c, Profiles of the total energies when moving the gold lead along these two directions with a fixed height (2.76 Å) from the line formed by the two Br atoms. L is the distance between two Br atoms along the sliding direction." Nevertheless, for completeness, we investigated theoretically the conductance evolution along the 'diagonal' direction using a larger 3x3x2 18Pb MAPbBr3 cluster (MA39Pb18Br75), as shown in Fig. S31. The diagonal sliding indicated by the red arrow and the junction conformations during this process are shown in Fig. S31a. The corresponding transmission functions and room-temperature conductances are presented in Fig. S31b and S31c. In common with the conductance evolution in the 'horizontal' direction, as the electrode slides along the 'diagonal' direction, the conductance initially decays exponentially, but just before rupture, there are two possible contact Br sites as presented in L-R4 a and L-R4 b . For L-R4 b , we again find a conductance jump at the end of the pulling, while there is no jump for L-R4 a Furthermore the 'diagonal' direction yields a higher factor of 0.87, compared with 0.58 along the 'horizontal' direction. The larger factor is a result of the weak coupling between the discrete Pb unit cells in the 'diagonal' direction.
To clarify this point, we added MAPbBr3, the sliding of the other electrode could go along all directions, e.g. giving two plateaus and then one jump, or several plateaus without a jump (see sliding directions above). The most common plateau is 3-step plateau. This is quite confusing to me.
Response: Thank you for your questions. Indeed, from the HRTEM image in Fig. S2 and S4, the QDs are not monodisperse. In other words, these QDs have various sizes and diameters. In fact, it is difficult to guarantee the QDs are monodisperse and all have similar diameters in the synthesis process even though the synthetic experiments were carried out in the glovebox and controlled the water and oxygen in the environment strictly. ( 7820-7823, (2015)) rather than the diameters of the QDs (3.75 nm or 6.32 nm). In addition, we also carried out control experiments of all the ligands and raw materials (Fig. S10) and no obvious conductance signals could be observed except PbBr2, indicating that only Br atoms can provide the binding sites of gold electrodes and the ligands outside the QDs have no impact on the charge transport of QDs. Therefore, as discussed above, it is reasonable to conclude that even though QDs are not monodisperse, this has no impact on their charge transport properties.
To further verify the above conclusions, we carried out the MCBJ measurements of MAPbBr3 QDs obtained from the centrifugal speeds of 5000 and 10000 rpm, respectively (as shown in Fig. S3). The HRTEM images suggest that the QDs obtained from the centrifugal speeds of 10000 rpm display the similar average diameters (6.34nm) to the centrifugal speeds of 5000 rpm (6.35 nm), while the former has the smaller standard deviation (1.35 nm) than the latter (2.27 nm), further proving that although the QDs are not monodisperse, the diameters and distributions of QDs do not affect the MCBJ experimental results.
To give a more detailed demonstration, we add the following sentences and the corresponding figures to SI: MAPbBr3 perovskite QDs with the centrifugal speed of 10000 rpm.

S3.9 MCBJ measurements of MAPbBr3 QDs with different centrifugal speeds
In order to prove that the sizes and diameters of QDs have no impact on their electrical properties, we carried out the MCBJ measurements using the perovskite quantum dots obtained with the centrifugal speeds of 5000 rpm and 10000 rpm (as shown in Fig. S3).
The MAPbBr3 QDs centrifuged with different centrifugal speeds express similar conductance values located at 10 -1.54 , 10 -2.80 and 10 -4.32 for 5000 rpm, 10 -1.43 , 10 -2.72 and 10 -4.28 for 10000 rpm, respectively, and the difference of adjacent statistical lengths matches well with the adjacent lattice distance of Br, which prove that the conductance plateaus we measured originate from the perovskite crystal cells rather than the entire perovskite QDs. with the centrifugal speed of 5000 rpm. The conductance-distance traces are recorded ~2500 traces. b. All-data-points 2D conductance versus relative distance (∆z) histogram for MAPbBr3 with the centrifugal speed of 5000 rpm. c. The displacement distributions of three plateaus for MAPbBr3 with the centrifugal speed of 5000 rpm. d. 1D Conductance histogram constructs without data selection for MAPbBr3 with the centrifugal speed of 10000 rpm. ~2500 conductance-distance traces are recorded. e.
All-data-points 2D conductance versus relative distance (∆z) histogram for MAPbBr3 with the centrifugal speed of 10000 rpm. f. The displacement distributions of three plateaus for MAPbBr3 with the centrifugal speed of 10000 rpm." In addition, we also added the following sentences in the manuscript: "In addition, we also carry out the MCBJ measurements using the MAPbBr3 QDs with the average diameters of 6.34 nm and 3.75nm, which are obtained from the centrifugal speeds of 10000 rpm and 5000 rpm, respectively (as shown in Fig. S3 and Fig. S17).
The experimental results show that the QDs with different diameters show similar conductance features, indicating that the conductance plateaus we measured originate from the perovskite crystal cells rather than the entire perovskite QDs." Regarding your concerns of the multiple possible binding sites during the sliding process of the gold electrodes, as we explained in the first response, the theoretical results show that the gold electrodes are more likely to slide along the 'horizontal' direction rather than the 'diagonal' direction due to the much lower the energy barrier.
In addition, the distance between two adjacent Br atoms along the 'horizontal' direction is in accordance with the experimental value.
It is possible that the gold electrode could go through one plateau, two plateaus, three plateaus and even more plateaus. The reason that more than three plateaus are not shown is due to the fact that the forth plateaus may be lower than the sensitivity limits of our set-ups. Furthermore, in order to analyze whether the 3-step plateaus are the most direction rather than the 'diagonal' direction.
To clarify this point, we have added the following sentences in the manuscript and SI: "In order to further analyze the possible binding sites of the gold electrodes during the pulling process, we use the spectral clustering algorithm to give comprehensive and detailed classifications of the individual conductance-distance traces. The original conductance-distance traces can mainly be divided into five categories (as shown in Fig.   S20 and S21 2. Define D to be the diagonal matrix whose (i, j)-element is the sum of A's i-th row, and construct the matrix L=D -1/2 AD -1/2 -I. c. This may also cause some issues on Fig. 3c, the displacement distribution, because not all the trace will follow the same direction across the QDs.
Response: Thank you for this nice suggestion. As mentioned in the above response, we have given a comprehensive classification of the traces using spectral clustering algorithms and obtained the relative displacement distributions. From these classification results, it is clear that although the three conductance plateaus do not appear at the same time in most cases, each plateau in different categories shows the similar displacement distributions, further confirming that the gold electrodes are more likely to slide along the "horizontal" directions rather than the "diagonal" directions.
d. In sum, I suggest the authors to carry out more analysis on their data. For example, the authors could analyze their traces and figure out the percentage of three plateaus/two plateaus/one plateaus, with or without the final jump. And then analyze all the traces in each category, to get the conductance value and displacement distribution. This could help resolving the issues of arbitrary contact sites.
Response: Thank you for this suggestion. As mentioned in the above response, we apply the spectral clustering algorithms to classify all the conductance traces in five categories and get the relative conductance values and displacement distributions in each category. In order to correlate each category to the possible binding sites, we expanded the theoretical models with different numbers of lattices (8Pb (MA20Pb8Br36), 10Pb (MA24Pb10Br44), 12Pb (MA28Pb12Br52) and 16Pb (MA36Pb16Br68)) and more binding sites (L a and L b To clarify this point, we added Table S2  However, the magnitude is much smaller in these two cases due to the higher barrier caused by the larger Br-Br distance."     (2) The authors should provide the chemical structure of 1 MAPbBr3 in Fig In addition, the MA represents CH3NH3 + , which has been explained in our previous version: "Four types of organic-inorganic halide perovskite QDs MAPbX3 (MA= CH3NH3 + , X=I -, Br -, Cl -, a mixture of Brand Cl -) are synthesized with oleic acid and octylamine as ligands to enhance colloidal stability and suppress QD aggregation effects." In order to make it clearer, we also added the corresponding explanation in the abstract: "Single-QD conductance measurements reveal that there are multiple distinguishable conductance peaks for the MAPbBr3 and MAPbBr2.15Cl0.85 QDs (MA= CH3NH3 + ), whose displacement distributions match the lattice constant of QDs, suggesting that the gold electrodes slide through different lattice sites of the QD via Au-halogen coupling." (4) The explanation of the sign dependence in quantum interference is a bit unclear. The text is too long and hard to understand. Authors may consider use one equation to explain it concisely (see Acc. Chem. Res. 2012, 45, 9, 1612-1621.
Response: Again, thank you very much for your valuable comments. We have removed these sentences from the previous version: "  Fig. 1b), then they will be constructive quantum interference (CQI) (high conductance) and when they have the same sign, they will be destructive quantum interference (DQI) (low conductance)." To accommodate your suggestion, we referred to the literature you mentioned (Acc. Chem. Res. 2012Res. , 45, 9, 1612Res. -1621 and changed the explanation of quantum interference effects as follows: The jump plateaus are shown by red frame. c, All-data-points 2D conductance versus relative distance (∆z) histogram of MAPbBr3 QDs (~3400 traces) and selected one conductance-distance trace. d, 2D relative conductance (G) verse relative displacement (∆z) histogram of the "jump curves" (~ 2400 traces) at the conductance-distance regime marked in Fig. 2c. The average diameters of MAPbBr3 QDs are 6.34 nm (Fig. S3b) and 3.75 nm (Fig. S2) (2016)).
However, the CH3NH3 + (MA + ) is located at the center of the regular octahedron, which is not easy to connect to the gold electrodes. The adjacent distance of the MA + is not in accordance with the displacement distributions. The electronegativity of the Pb 2+ is low, and the Pb 2+ is hidden within the Br networks that could not have reliable interaction with the gold electrodes. Therefore, both theoretical calculation and single-molecule conductance measurements suggests that the conductance plateaus of the single-QD junction originate from the Au-Br interaction sliding on the surface of the different lattice sites rather than the surface Br ions along with the ligands or the migration of Br ions.
To clarify this point, we have added these sentences in the manuscript: "As for the other atoms, the MA + is located at the center of the regular octahedron, which is not easy to connect to the gold electrodes, and the adjacent distance of the MA + is not in accordance with the displacement distributions. The electronegativity of the Pb 2+ is low, and the Pb 2+ is hidden within the Br networks that could not have reliable interaction with the gold electrodes. Therefore, the gold electrodes interact with halogen, rather than other atoms or groups, to form stable Au-QD-Au junctions." (2) I also have concerns about the QD structures in the computation, as mentioned above, the information of organic ligands is completely missing, can these structures represent the ones in the experiments? Intuitively, I think the organic ligands have impacts on the interaction between gold and QDs, also the electronic structure of QDs.
Response: Thanks for your suggestion. In order to address this question, we carried out new calculations of 12Pb with ligands to prove the negligible influence of the ligands on the charge transport process of QDs. Five typical conformations were considered: a.
1 octylamine, b. 2 octylamines, c. 1 oleic acid, d. 2 oleic acids, e. 1 octylamine and 1 oleic acid. All of these five cases reveal that the ligands barely influence the transmission function, because of the weak interaction between the ligands and the perovskite quantum dot. As shown in Fig. S32, we place the ligand molecules close to the cluster and then relax these molecules, while freezing the perovskite cluster and the gold atoms. The transmission functions are presented on the right side in Fig. S32. For the oleic acid, the transmission function is nearly the same as the bare 12Pb cluster. For octylamine, a resonance appears at the position close to HOMO. However this will not influence the conductance since it is far from the Fermi energy. We also considered the case in which the ligand molecule bridges the gold electrode and the cluster to investigate the influence of ligand molecule on the coupling. The results are shown in   (2019)) Therefore, we believe our experimental data is convincing, highly repeatable and supports the conclusions of this work.
Furthermore, in order to confirm that the measurement is robust and highly reprodubile, we also carried out the MCBJ measurements on a few pure Br-based QD samples with different sizes and diameters. We obtained the MAPbBr3 perovskite QDs at the centrifugal speed of 5000 and 10000 rpm, respectively (as shown in Fig. S17). The experimental results show that perovskite quantum dots with different sizes display similar electrical properties, which proves that the conductance plateaus we measured originate from the perovskite crystal cell and the sizes and diameters of QDs do not affect the single-molecule experimental results. These results also give strong evidence that our experimental data is highly repeatable and well supported.
To give a more detailed demonstration, we have added the following sentences and the corresponding figures to the SI as section S3.9: "S3.9 MCBJ measurements of MAPbBr3 QDs with centrifugal speeds

In order to prove the sizes and diameters of QDs have no clear impact on their electrical
properties, we carry out the MCBJ measurements using the perovskite quantum dots obtained with the centrifugal speeds of 5000 rpm and 10000 rpm (as shown in Fig. S3).
The MAPbBr3 QDs centrifuged with different centrifugal speeds express similar conductance values located at 10 -1.54 , 10 -2.80 and 10 -4.32 for 5000 rpm, 10 -1.43 , 10 -2.72 and 10 -4.28 for 10000 rpm respectively, and the difference of adjacent statistical lengths matches well with the adjacent lattice distance of Br, which prove that the conductance plateaus we measured originate from the perovskite crystal cells rather than the entire perovskite QDs. Conductance histogram constructs without data selection for MAPbBr3 with the centrifugal speed of 10000 rpm. The conductance-distance traces are recorded ~2500 traces. e. All-data-points 2D conductance versus relative distance (∆z) histogram for MAPbBr3 with the centrifugal speed of 10000 rpm. f. The displacement distributions of three plateaus for MAPbBr3 with the centrifugal speed of 10000 rpm." We also added the following explanation in the manuscript: "In addition, we also carry out the MCBJ measurements using the MAPbBr3 QDs with the average diameters of 6.34 nm and 3.75nm, which are obtained from the centrifugal speeds of 10000 rpm and 5000 rpm, respectively (as shown in Fig. S3 and Fig. S17). We have added the following to the SI: "S3.10 The supplementary data of 1D conductance histograms of MAPbBr3 QDs In order to confirm that the experimental data we measured has high repeatability and quality, we repeated the MCBJ measurements of MAPbBr3 QDs several times at different bias voltages. The experimental data presents that all 1D conductance histograms display three or four clear conductance plateaus with small standard deviations, suggesting that the experimental data is highly reproducible and robust.    (2015)).
To clarify this point, we added these sentences in the manuscript: "We also carry out DFT calculations for MAPbCl3 and MAPbI3 QDs. Our results show that the three halide perovskite QDs possess similar charge transport features (see Fig.   S26 and S27 in SI). However, as mentioned above, in a real experiment they are not "After relaxation, the optimized separation between contact halogen atoms (Cl, Br, I) and apex gold atom were found to be 2.66 Å, 2.76 Å and 2.88 Å respectively."  This manuscript has demonstrated experimental and theoretical investigation of room temperature QI effects in the electron transport through single perovskite QD junctions.
Three distinct conductance features are observed from the conductance measurements of perovskite QDs with Br, while the QDs with I and Cl show no significant features.
The multiple conductance features are derived from the sliding of gold electrodes between the adjacent Br atoms in different unit cells. A distinct conductance jump at the end of individual conductance traces, which is claimed as room-temperature QI effects. Basically this is interesting work and could possibly published in Nature Communications only after the following points are considered.
(1) The distinct conductance jump at the end of individual conductance traces is very interesting and owing to the junction switch from "L-R3" to "L-R4". However, this is ideal case only for three lattices. From the TEM images of Fig. S2 and S3, the QDs are not uniform enough. To support the authors' conclusion, more cases with different numbers of lattices should be included. Then the conductance jumps may appear after two or four (and so on) conductance plateaus.  Y., et al. Chem. Commun. 51, 7820-7823, (2015)) rather than the diameters of the QDs (3.75 nm or 6.32 nm).

Response
To further verify the above conclusions, we carried out the MCBJ measurements of MAPbBr3 QDs obtained from the centrifugal speeds of 5000 and 10000 rpm, respectively (as shown in Fig. S3). The HRTEM images suggest that the QDs obtained from the centrifugal speeds of 10000 rpm display the similar average diameters (6.34nm) to the centrifugal speeds of 5000 rpm (6.35 nm), while the former has the smaller standard deviation (1.35 nm) than the latter (2.27 nm), further proving that although the QDs are not non-uniform, the diameters and distributions of QDs do not affect the MCBJ experimental results.
To give a more detailed demonstration, we add these sentences and the corresponding figures to the SI:

S3.9 MCBJ measurements of MAPbBr3 QDs with centrifugal speeds
In order to prove the sizes and diameters of QDs have no impact on their electrical properties, we carry out the MCBJ measurements using the perovskite quantum dots obtained with the centrifugal speeds of 5000 rpm and 10000 rpm (as shown in Fig. S3).
The MAPbBr3 QDs centrifuged with different centrifugal speeds express similar conductance values located at 10 -1.54 , 10 -2.80 and 10 -4.32 for 5000 rpm, 10 -1.43 , 10 -2.72 and 10 -4.28 for 10000 rpm, respectively, and the difference of adjacent statistical lengths matches well with the adjacent lattice distance of Br, which prove that the conductance plateaus we measured originate from the perovskite crystal cells rather than the entire perovskite QDs. Conductance histogram constructs without data selection for MAPbBr3 with the centrifugal speed of 10000 rpm. The conductance-distance traces are recorded ~2500 traces. e. All-data-points 2D conductance versus relative distance (∆z) histogram for MAPbBr3 with the centrifugal speed of 10000 rpm. f. The displacement distributions of three plateaus for MAPbBr3 with the centrifugal speed of 10000 rpm." In addition, we also added the following explanation in the manuscript: "In addition, we also carry out the MCBJ measurements using the MAPbBr3 QDs with the average diameters of 6.34 nm and 3.75 nm, which are obtained from the centrifugal speeds of 10000 rpm and 5000 rpm, respectively (as shown in Fig. S3 and Fig. S17).
The experimental results show that the QDs with different diameters display similar conductance features, indicating that the conductance plateaus we measured originate from the perovskite crystal cells rather than the entire perovskite QDs." On the other hand, we agree with your statement that "more cases with different numbers of lattices should be included to support our conclusion". Indeed, it is possible that the gold electrode could go along all directions and the conductance jumps may appear after two or four (and so on) conductance plateaus. Actually, from the theoretical results of Fig. S26 and Fig. S27  S38-S39), the conductances of MAPbBr3 are below the detection limit of our instrument (10 -6 G/G0). The theoretical distances of these cases ( > 15 Å) are also much larger than the experimental displacement distributions (maximum 12 Å). Therefore, the theoretical cases with too low conductances and too long distances can be excluded from the experimental results, and our theoretical models with 18Pb clusters are sufficient to reflect the vast majority of possible experimental cases.
To further provide the possible theoretical models of the perovskite QD junctions, we added Table S4    To clarify this point, we have added these sentences in the manuscript and SI: "In order to further analyze the possible binding sites of the gold electrodes during the pulling process, we use the spectral clustering algorithm to give comprehensive and detailed classifications of the individual conductance-distance traces. The original conductance-distance traces can mainly be divided into five categories (as shown in Fig.   S20 and S21 (2) Three exposed halogen atoms on the corner lattice had the opportunity to interact with the gold electrodes. One of them was labelled as "L" in this work. The authors only assumed and calculated one ideal case. How about the other two cases for the "L" atom in two orthogonal directions? The conclusion from just one special case is not convinced enough since the authors cannot precisely control the junction between the QD and the Au electrodes.
Response: Thanks for this nice suggestion. In order to simplify the theoretical models and reduce the computational burden, we fixed the left gold electrode and changed the sites of the right gold electrode to simulate the sliding process in the real experiments.
In fact, from the theoretical results of Fig. S27-S29 in the previous version, we have shown three different fixed sites of the left gold electrode for 2x2x4 16Pb clusters and the results have been explained in the manuscript.
"Other possible connectivities for 16Pb MaPbBr3 cluster are also explored (Fig. S27 and Fig. S28), we find that this jump behaviour is generic although different factors are observed (0.72/Å and 1.2/Å separately), and the latter connectivity is less likely to appear in the experiments due to the higher energy barrier." However, we only consider the cases that the two gold electrodes are connected to the two closest Br atoms at the beginning of this pulling process. This is because, in real experiments, after the rupture of the gold wire, the initial gap width is known to be a snap-back distance of about 5 Å. Since this corresponds to the distance between two closest Br atoms (around 5 Å), these two Br atoms are most likely to be connected to the gold atoms at the beginning in this pulling process.
Nevertheless, for completeness, two new left binding sites (L a and L b ) were considered in the new calculation. The gold electrodes in these cases are not connected to the two closest Br atoms at the beginning of the pulling process. As shown in Fig. S38 and Fig.   S39, we find the conductance evolution follows the same trend as the case of the left contact Br atom (L), ie it first decays exponentially and then jumps at the end. However, the magnitude of conductances is much smaller in these two cases due to the higher barrier caused by the larger Br-Br distance. In addition, the conductances of the cases L a -R1 and L b -R1 are also much smaller than our experimental results. Therefore, it is reasonable to conclude that the gold electrodes are more likely to connect to the two closest Br atoms at the beginning of the junction formation.
To clarify this point, we added Fig. S38 and S39 in SI, and these sentences in manuscript: "Two new left binding sites (L a and L b ) were also considered in our calculations. As shown in Fig. S38 and Fig. S39, we find the conductance evolution follows the same trend as the binding sites of L, ie it first decays exponentially and then jumps at end.
However, the magnitude is much smaller in these two cases due to the higher barrier caused by the larger Br-Br distance."   (2015)), the MAPbBr3-xClx QDs are the first choice to investigate the quantum interference effects and further confirm the binding sites through Au-Br interaction during the MCBJ measurements.
In addition, in order to provide further evidence that the Au-I interaction cannot form the stable single-QD junction, we carried out the MCBJ measurements with MAPbBr3-xIx QDs and added the following sentences in the SI as section S3.8: "S3.8 MCBJ measurements of MAPbBr2.15I0.85 QDs In order to provide further evidence that the Au-I interaction cannot form the stable single-QD junction, we have also measured the electrical properties of MAPbBr2.15I0.85 perovskite QDs. The experimental results show that neither the peak of gold-gold atomic junction nor the conductance plateaus of the single-QD junction can be observed in MAPbBr2.15I0.85 QDs, which is similar to the charge transport properties of MAPbBrI3 QDs. Therefore, it can be demonstrated that the Au-I interaction cannot form stable single-QD junctions due to its stronger bond energy and poorer stability of the crystal structure.