Peer review of: In situ nanoscale imaging of moiré superlattices in twisted van der Waals heterostructures (2020)

REVIEWER COMMENTS 

Reviewer #1 (Remarks to the Author): 

In this manuscript, Luo et al. reported the characterization of h-BN encapsulated twisted bilayer 
graphene heterostructure by s-SNOM. Through the measurement of the buried heterostructure, 
the hyperbolic h-BN phonon polaritons launched in the h-BN layer interacting with the moiré 
structure in the twisted bilayer graphene was explored. By comparing experimental results and 
theoretical calculations, the influence of domain walls and the formation mechanism of the 
hyperbolic phonon polariton are interpreted. Their results are novel and should attract interest 
from many researchers in the fields of 2D materials. However, there are several points that need 
to be clarified before this work is considered for publication. 

1. Line 108, what is the meaning of “the type II region”. Where is “the type I”? What is their 
difference. 
2. In Fig 3a, there are two symmetric peaks formed at the both sides of domain walls. Does this 
mean that the domain walls have inherent width? If the width of the domain walls cannot be 
ignored, its influence on the value of dpeak here should be considered. 
3. As shown in Fig 4c, there are second-order peaks observed in the calculation results. Why the 
second-order peaks are not seen in the experimental results. Pls explain. 
4. Line 119, “Note that since we are now imaging the domain walls in TBG through nonaligned h-
BN layers, the top layer thickness is no longer limited to less than 4nm in order to excite the SPP 
in graphene layer.” May I know the reason why the top layer thickness should be less than 4nm if 
the graphene/hBN has a very small separation angle ([Nature Communications 6, 6499, 2015.] 
[Nature Materials 14, 1217–1222, 2015.]). 
5. Line 29, there are two “in” in the sentence. 
6. Information of scale bars in Fig 1c-e, 2a is missing. 
7. In Fig 3b, it shows the laser frequency of 1580cm-1, while it mentioned in the manuscript is 
1530cm-1 (line 171). Pls double check. 



Reviewer #2 (Remarks to the Author): 

The article “In-situ nanoscale imaging of moiré superlattices in twisted van der Waals 
heterostructures” by Y. Luo et al. demonstrates that the moire pattern in twisted by-layer 
graphene can be indirectly imaged by imaging the phonon polariton interference on the top hBN 
encapsulation layer. Due to optical conductivity difference in the domain wall, the measured 
polariton interference image is reminiscent to the underlying moire pattern. This nondestructive 
imaging method shows several advantages over other commonly used imaging techniques such as 
STM, TEM, and PFM. 
The authors provided sufficient experimental evidence as well as simulation and modelling efforts. 
I don’t see major technical issues. However, the resolution of this imaging technique seems to be 
limited by the tip radius and phonon polariton wavelength to ~80 nm, which means samples with 
larger twist angle is not applicable. Currently, the more interesting samples typically have larger 
twist angle, namely ~1.1 degree for obvious reasons. Therefore, I foresee the usefulness of the 
proposed imaging technique to be very limited. Besides, I list several more detailed issues below: 
1. The length of the scale bars in Figure 1 c, d, and e are missing, therefore it’s unclear how large 
the moire pattern is. The twist angle is also not mentioned. 
2. In Figure 2 c the calculated spectra are maximum in the |r_p|^2. The authors claim this 
qualitatively reflects the near-field signal. I wonder if any previous work or theory can support this. 
3. The simulated spectra in Figure 2 c are obtained by simulating a pyramid shape tip above the 
sample. There are several problems. 
• First of all, the authors did not specify the tip parameters like length, apex radius, opening angle, 
etc. Boundary conditions, sample size etc are not mentioned as well. 
• Secondly, the power absorbed by the sample is calculated by the power field monitor between 
the tip and sample. Why does it reflect the near-field scattering? 
• What’s the tip-sample distance? 
• How is the oblique incident angle handled in the simulation? When calculating a broadband 
oblique incidence, the incident angle is usually not uniform using a FDTD solver. 
4. In line 154, the sentence reads “Line profiles are acquired perpendicular to the edge of the 
heterostructure allow measurement of the polariton wavelength (Fig. 2f).” There is some grammar 
issue with this sentence. 
In general, I believe this manuscript by Luo et al. presents a nice work on electontronic moire 
patterns in graphene using near-field mapping of the hBN polaritons. The results are solid but no 
new physics insights have been provided. I recommend major revision. 



Reviewer #3 (Remarks to the Author): 

In the manuscript “In-situ nanoscale imaging of moiré superlattices in twisted van der Waals 
heterostructures,” Y. Luo et al., have addressed the reflection of phonon-polaritons in hBN off of a 
buried soliton lattice in TBG. Overall, I believe the topic is interesting and important. However, the 
manuscript lacks clarity and sufficient detail to fully understand the advances claimed within this 
work. I believe that significant revisions are needed before the work is ready for publication. 

1. Emphasis is placed on the utility of non-destructive imaging of nano-meter scale properties in 
moiré superlattices in van der Waals (vdW) heterostructures. Yet the authors technique is limited 
to extremely small twist angles <0.250, which is well below the magic angle, and limits the 
potential utility as a characterization tool. Do the authors have a suggestion for how the technique 
can be extended to larger twist angles? 

2. One of the main advantages emphasized by the authors appears to be the ability to interrogate 
moiré patterns in TBG through slightly thicker (8-16 vs. 4 nm) hBN capping layers. It is claimed 
several times that the domain walls cannot be imaged through hBN top layers thicker than 4 nm 
with the method demonstrated by S. Sunku et al. Yet in the authors own Fig 1d the domain walls 
from the AB/BA domains can be observed at 940 cm-1, which is outside of the reststrahlen band 
of hBN. Are the measurements presented in Fig. 1d and e performed on the same device with the 
same doping level? The authors should clarify or modify their claims. 

3. The authors note that the previous work of Sunku et al., has the disadvantage that the 
graphene layer must be sufficiently doped (lines 56 to 60). In the present work the graphene is 
also doped (~50 meV). Are the authors claiming that the doping of their device is unimportant? 
Can the authors clarify how doping impacts the nano-infrared contrast? 

4. The authors invoke a ~0.2 eV resonance in the optical conductivity to explain the nano-infrared 
spectroscopic results at the domain wall. The authors should state their procedure for normalizing 
the data presented in Fig. 2b as it is essential to the conclusions. It is also not so obvious what is 
the influence of the propagating polariton mode on the spectra recorded near the ‘DW location’. A 
hyperspectral line scan across the domain wall may be more appropriate for this situation. 

5. The frequency dependent optical conductivity is used to model the nano-optical spectra with a 
rather un-conventional method of comparing the absolute value of Rp at the first order maxima of 
the hyperbolic polariton in hBN to, qualitatively, explain the experimental data of the near-field 
amplitude. Why did the authors not use the lightning rod or even point dipole model? As is, a 
complete explanation as to what the precise meaning of, and we can learn from, the Rp 
comparison is merited. 
6. The authors also use FDTD, described in Supplementary Note 4. The latter section describes in 
great detail what was simulated. However, it does not clarify if the simulations of z-component of 
the electric field were put through a demodulation scheme to arrive at the trend displayed in Fig. 
2c and does not clearly state what is plotted. Thus, it would help to clarify what exactly is plotted 
in Fig 2c and provide an appropriate label of the vertical axis. The end result is claimed to 
qualitatively resemble the experimental data reproducing the observation that ‘the resonance 
mode is damped and blue shifted.’ Which appears dodgy as enhancement of the near-field 
amplitude is maximal at whatever frequency \beta [Ref-McLeod PRB 90, 085136 (2014)] is 
maximal and an apparent ‘shift’ in the amplitude spectra could be caused by a dispersion-less 
offset of the optical conductivity. The spectra may be further complicated by the propagating 
polariton as in comment 4. Thus, I have several questions. Is the calculated optical conductivity 
capable of explaining the DW contrast observed at 940 cm-1 in Fig 1d? Is a resonance in the 
optical conductivity at 0.2 eV essential to explain the experimental findings, or is the motivation 
for the latter resonance purely theoretical? Is the predicted resonant frequency dependent on the 
twist angle of the TBG? 

7. The authors may wish to address momentum in the introduction of launching polaritons with s-
SNOM (lines 75-78). As written the text could be interpreted as polaritons are launched because of 
the enhanced electric field. “The appropriate mid IR frequency” is, also, not clearly defined. 

8. The sentence “This advance offers the ability to image the physics of pre and post processed 
devices undertest” (line 86) appears dodgy. What does the statement “image the physics” mean 
precisely? 

9. Several other phrases are somewhat obscure: 

a. Line 25 ‘spatially dependent field profile’ – what field? 
b. Line 85 ‘quasi-particle dynamics’ – what dynamics are the authors referring to? The utility of 
dynamic hybridization has furthermore been pointed out by several authors, including buried 
surfaces [see for example, K. Chaundhary et al., Science Advances 5, eaau7171 (2019)]. 
c. Line 139 ‘the smallest perturbation is sufficient to create an efficient scattering mechanism.’ The 
meaning of ‘the smallest perturbation’ is unclear, which relates to comment 2. 
d. Line 221 ‘electronic topology’ appears very suddenly and its relevance to the discussion is not 
clarified within the text.