Peer review of: Structural order in plasmonic superlattices (2020)

<b>REVIEWER COMMENTS</B> 

Reviewer #1 (Remarks to the Author): 

The paper by Schulz et al. report on the fabrication of plasmonic superlattices and their optical 
characterization. The results shown in the manuscript are really interesting since they have combined 
the synthesis of gold spheres with high monodispersity together with slow evaporation of toluene over 
a DEG leading to plasmonic superlattices that in agreement with the simulations support collective 
plasmon polariton modes. The manuscript is interesting and the resulst shown clear but there are a 
number of points that need to be clarified prior to support its acceptance. 
- To what extent can the number of layers be controlled?, which are the critical parameters for that?. 
- When reporting the optical properties of the layers I think that there a lot of missing information; in 
Fig 4 is reported the reflectance of trilayer, the same data should be given a single monolayer also for 
a bilayer (together with the FDTD simulation). Which is the influence of the PSS length on the optical 
response of the plasmon polariton?. 
It would be interesting also provide X axis in terms of nm apart from eV. Reporting also the 
absorbance or the transmittance will help the reader. 
Related with the optical properties, and considering the tight control that the authors reported I think 
that a similar data to that mentioned above should be also give for the different sizes and the different 
PSS sizes. 
In summary, I think that the manuscript could be considered for publication but a more deep study 
and analysis of the optical properties of the different systems that the authors claimed can be 
fabricated need to be reported. 



Reviewer #2 (Remarks to the Author): 

The manuscript by Schulz et al. titled "Structural order in plasmonic superlattices" addresses two of 
the fundamental issues in the field of nanoparticle (NP) self-assembly, namely (i) the fabrication of 
organized, possibly defect-free two- and three-dimensional arrays of NPs with long-range order and (ii) 
the subsequent control of the interparticle separation distances, so as to modulate the collective 
properties of the ensemble, such as, e.g., its plasmonic/polaritonic ones. Common strategies to 
achieve these goals involve functionalization of the NP surfaces (i) with polymers of different lengths 
(as in this study), (ii) with DNA [see, e.g., Liu et al., Science 351, 582 (2016)], and (iii) with dendritic 
molecules of various generations [see, e.g., Malassis et al., Nanoscale 8, 13192 (2016)]. 

As acknowledged by the authors in their manuscript, many related studies have been reported so far, 
and the employed experimental techniques they use are a priori routine, which may suggest that the 
present work lacks originality and novelty. However, the presented results constitute in my opinion a 
very interesting contribution to the field, as Schulz et al. obtain, to the best of my knowledge, an 
unprecedented long-range order of the gold NP lattice. These results pave the way to promising 
prospects for, e.g., plasmonic metamaterials. Additionally, the manuscript is well written and reads 
well. Consequently, I would in principle recommend publication in Nature Communications. However, 
there are some elements of the discussion that I believe are not fully convincing and which should be 
clarified before the final publication of the manuscript. 

1/ In particular, the different interparticle gaps measured for NPs of various sizes but bearing the 
same ligand are ascribed to stronger attractive interactions between Au NPs as their diameter is 
increased (see the discussion around Fig. 2). As recognized by the authors (see lines 133 and 134), 
this may be true for series with PSSH12k, where a linear gap-diameter relation is found (see Fig. 2), 
but not for PSSH5k: as the NP diameter increases from ca. 25 to 60 nm, the gap varies in a sawtooth 
manner for the series PSSH5k (3.3, 5.1, 1.3, and 2.2 nm, see Table 1). The results for PSSH2k are 
not conclusive, since only two samples were considered. I therefore wonder if Fig. 2, which only 
presents results for PSSH12k, is not slightly misleading. While it is plausible that van der Waals forces 
are at work in explaining the data in Fig. 2, why should it also be the mechanism able to interpret the 
PSSH5k series, given the nonmonotonic gap-size relation in that case? 

2/ For the larger NPs in Table 1, the gaps lie in the range of the mean standard deviation found for the 
NP diameter. I therefore wonder if these results obtained by TEM measurements are meaningful for 
such large NPs. Probably, these results should be compared with the lattice constant a obtained from 
the SAXS ones. It would also be useful in Table 1 to provide the results of the SAXS measurements 
(when available, since apparently only 5 samples out of 10 were measured). 

In addition to my two comments above, I also have several remarks and questions on the present 
manuscript that should certainly be addressed by the authors: 

3/ Refs. 9 and 10 are exactly the same. 

4/ On line 46, the authors state that "According to simulations, the coupling strength (...)". To which 
simulations are they referring to? Those in Refs. 25-27? This is slightly ambiguous. 

5/ On line 93, the authors mention "Murray's group" when introducing the work presented in Ref. 44. I 
must admit that I find this wording quite unfortunate and slightly discourteous for the 1st author of 
Ref. 44 (who probably did most of the work). I would rather for instance employ the wording "Dong et 
al." which gives full credit to all contributing authors, and not only to the group leader. 

6/ Fig. 1b is, at least on a printed version of the manuscript, way too small, so that it is very difficult 
to see the actual sample. 

7/ About the measured reflectance spectrum shown in Fig. 4, the angle of incidence should probably 
be specified. 

8/ On line 185, the authors claim that "[their] experimental spectra are in excellent agreement" with 
FDTD simulations obtained with the commercial software package Lumerical. However, even though 
the simulation (dashed black line in Fig. 4) is in fairly good qualitative agreement with the 
measurement (solid blue line), I would not say that the agreement is "excellent", as there are still 
significant quantitative differences between the two curves (see, in particular, the "down" peak feature 
at around 1.5 eV, where the measured reflectance is of about 25%, while the simulation predicts 50%, 
that is, a factor of 2 larger). 

9/ Still about the results presented in Fig. 4: the simulations predict a vanishing reflectance for an 
excitation energy around 1.1 eV, while the measured reflectance is finite and equals roughly 10%. 
Could the authors comment on this qualitative disagreement? 

10/ In Fig. 5, one can observe a small energy shift between the two curves for the polaritonic mode at 
around 1.5 eV. Can it be due to the two different dielectric environments produced by the two 
different ligands, and the subsequent effect on the localized plasmon resonance frequency of the 
individual NPs (which itself influence the collective polaritonic modes)? 


Reviewer #3 (Remarks to the Author): 

“Structural Order in Plasmonic Superlattices” by F. Schultz et al 

The authors, propose and deeply investigate highly ordered plasmonic arrays and multilayers of these 
arrays. A wide variety of arrays of plasmonic NPs have been proposed, synthesized, and studied by a 
large number of groups. From small to large NPs, from small to large lattice parameters, …. While 
some groups succeeded in obtaining well controlled NP separation, others succeeded in the fabrication 
of large scale arrays or highly uniform NP shape/size. Here, the authors succeeded at fabrication 
highly ordered, almost defect free of highly NPs with very homogeneous size and shape, and this on a 
large scale. 
In itself this warrants publication of these results as the proposed fabrication procedure will have a 
strong impact on a large community seeking robust NP-based platform for a wide range of application. 

I do think the authors could have done a slightly better job at placing their work in context as major 
pioneer works are not cited and/or discussed (e.g.: work by Mirkin on DNA-based superlattices, and 
Odom on 2D NP arrays), including work on bi-metallic superlattices (Ross et al, Nat. Comm. 2016). 
The recent review paper by Liz Marzan (Acc. Chem. Res 2019) is also to be cited along with the 2006 
Nature paper by Chris Murray. 

Also, although the authors compare their experimental reflectance measurement to some FDTD 
simulation, there’s very little comparison to theoretical predictions of the superlattice properties. If the 
lattice are highly ordered, with very little size, shape, and gap variation throughout the array, a more 
robust and systematic comparison with theory/simulation would strengthen the authors’ conclusions 
even more. I know the authors have already recently published theory papers on these systems, but a 
better discussion and closer comparison between the two would be very interesting here. 

Although the authors reference the FDTD method section to previous papers, I think it is important 
that the authors briefly summarize the numerical protocol and model in this section so that the reader 
can quickly get a sense of how the numerical modeling is done. 

Apart from these, the results are very convincing and show tremendous potential for future 
applications. I personally wondering how straight forward it will be be to extend this approach to other 
materials (Ag, Al, Pd,…). Also, although the authors briefly mention it at the end, I would recommend 
the author to briefly discuss how their approach could be expanded to anisotropic NPs such as cubes, 
rod/ellipsoids, prisms for instance. 

In short, I strongly recommend publication of this work in Nature Communication.