Peer review of: Quantum-dot assisted spectroscopy of degeneracy-lifted Landau levels in graphene (2020)

REVIEWER COMMENTS 

Reviewer #1 (Remarks to the Author): 

Keren et al. introduce a novel and very interesting spectroscopic technique for the study of layered 
2D van der Wall's devices and apply it to monolayer graphene. Using a very thin hBN dielectric 
they obtain a tunneling current, between the graphene and a graphite bottom gate which serves 
as a source, only through individual hBN defects acting as quantum dots. This allows them to 
probe the local density of states in the sample in a manner not wholly dissimilar to STM, but 
without the seemingly unavoidable tip gating of the latter technique. The results which they on the 
splitting of the Landau levels obtain at high magnetic fields are also of significant interest. 

The explanation of their tunneling setup seemed to me quite thorough and detailed, and backed by 
algebra which is rather easy to understand and thoroughly worked out in the supplementary 
information. One minor quibble is that in Fig. 1(a) the source voltage is labeled V_SD which might 
lead to confusion, as in the text this is uniformly designated V_Src. 

There are some things which I wish the authors could elaborate. One thing which I think would be 
useful to workers would be related to the frequency of occurrence of these quantum dots in the 
hBN. In Fig. 1 is shown data in which (as the simulation makes especially clear), the existence 
even of a second dot significantly complicates the observations; ideally one would have only one 
dot whose level participates in the tunneling. One supposes that these dots must occur in a 
somewhat random pattern depending on the quality of the hBN, but on average there should be a 
certain number of them per unit area and for this purpose it would be useful to know what was the 
actual area of the thin hBN barrier in this experiment; if it was in the paper I must have missed it. 
(Even a microscope picture of the device, perhaps added to the supplement, would help here.) If 
the authors would go further and try to estimate based on their experience how "lucky" one has to 
be in order to find a thin hBN flake with only one or two defects through which tunneling occurs, or 
the procedures used to obtain such a flake with the greatest likelihood, it would be useful for 
specialists. 

Another question that comes to mind is if the authors could estimate (perhaps via a calculation) to 
what degree a circular potential in the graphene might be induced by the presence of the dot, and 
what effects this would have on the experimental data. (e.g., could any of the features in the 
experimental plots be explained by such degeneracy lifting? I am thinking for example of the flock 
of nearly horizontal peaks within the N=1 box of Fig. 3(a)). In any case I suppose the circular 
potential from the dot should be less overbearing than that of an STM tip, and does not 
compromise the utility of the new technique. 

In summary, I find the technique and also the experimental data very interesting and worthy of 
publication, and I hope the authors can address some of the above technical points. 


Reviewer #2 (Remarks to the Author): 

This paper provides a defect-dot-assisted tunneling method to probe the Landau level 
spectroscopy of graphene and reveals energy split in the N = 0 and N = 1 excited Landau levels in 
the presence of a magnetic field. An energy split with Landé g-factor as high as 160 is observed in 
the N = 0 excited Landau level, and a split with g=36 is measured in the N = 1 excited level. 
Under high magnetic fields at 20 T and 33 T, four distinct split-levels also with large split gaps are 
observed and are attributed to the four-fold degeneracy lifting of graphene. The authors claim that 
the large splitting in energy levels is a consequence of enhanced exchange interactions. 

The provided experimental technique is quite interesting, and the analysis is of very high quality. I 
am inclined to recommend its publication to Nature communications. However, I would like to urge 
the authors to address the following issues before I can make my recommendation. 

1. How thick the hBN barrier used in experiment is? It is that mentioned in page 7 “We find the 
barrier thickness to be dSrc = 2 nm, likely 3 layers of hBN”? I think it would be better to describe 
it more clearly in the beginning or in the Device Fabrication. 

2. Are all the experimental data measured in one sample? Did the authors find similar results in 
other samples with different hBN barrier thickness? What’s the effect of the barrier thickness on 
this tunneling measurement? 

3. Why do dot1 and dot2 show so different results in Fig.1 and Fig.2？Whether it means that the 
dot-assisted tunneling depends on different dots? If so, depending on what parameters of the dot? 

4. The valley splitting is nearly constant from 4T to 10T for the N=0 level in Fig. 3(f), and it shows 
an increase from 20T to 33T for the N=1 level in Fig. 4(f). What results in such a difference? And 
what’s the origin of the valley splitting observed in this experiment? 

5. In the first paragraph of page 15, the authors state that “It is evident that in all fill factors the 
gap between spin-down states (blue markers) barely changes”. It seems that the gap between 
spin-down states presented in Fig. 4(f) also shows an increase with increasing the magnetic field. 

6. Recently, several STM works reported the studies of the Landau level splitting in bilayer and 
trilayer graphene and shown large g factor for high-bias levels. The authors should mention these 
reports. 

Minor points: 

7. The authors define the bias voltage between the graphite and graphene flakes as VSrc, but such 
a bias is marked by VSD in the schematic illustration Fig. 1(a). It would be better to use an 
identical definition. 

8. For the statement “Plotted as a yellow dashed line in panel (c)” in the second paragraph of page 
10, the authors should point out clearly that which figure’s panel (c) they want to indicate (It 
should be Fig. 2(c) I think).