Peer review of: Ultra-fast vortex motion in a direct-write Nb-C superconductor (2020)

Reviewers' comments: 

Reviewer #1 (Remarks to the Author): 

This work reports extensive transport measurements of the flux flow instability which was interpreted 
in terms of the Larkin-Ovchinnikov (LO) instability affected by the edge barrier. This study extends 
many previous experimental investigations of the LO instability to a narrow film Nb-C film strips with 
controlled edge barrier properties which allowed the authors to extract the vortex velocities of the 
order of 10 km/s at the onset of instability. The results appear interesting and qualitative conclusions 
are supported by the experimental data, so this work in my opinion would be appropriate for Nature 
Communications. Yet the authors focused on a particular scenario, while disregarding other effects 
which can affect the valued of the parameters extracted from model fits, so the key assumptions 
should be clarified, as outlined below. 

1. The field dependence Ic(B) \propto B^{-a} with a ≈1/2 observed at B > 100 mT has been often 
observed on superconducting films. It follows from many models of bulk pinning [see, e.g., PRB, 66, 
024523 (2002); 73, 134502 (2006)] if the applied field B is much greater than the self-field Bs. At low 
fields B < Bs the mean density of vortices across the strip becomes inhomogeneous, which obviously 
affects the field dependence of Ic(B) even if the edge barrier is not taken into account. The self-field 
effects can thus contribute to the observed crossover of Ic(H) below 50 mT which may not entirely 
result from the edge barrier pinning. The contribution of the self-field effects should be estimated and 
discussed. 
2. On p.10, where it is said that “Ic \propto 1/B is a fingerprint of edge pinning”, a reference should be 
given. Moreover, the field dependence Ic \propto 1/(B0+B) is not exclusively characteristic of the edge 
pinning but has also been observed on different superconductors for more than 60 years (the so-called 
Kim model), see, e.g. a review by Campbell and Evetts or else. 
3. Analysis of experimental data was done assuming uniform distributions of vortices, which is hardly 
the case. In the edge barrier pinning scenario the onset of resistivity correspond to vortices 
penetrating locally through materials defects at the edges and forming “rivers or trees” of magnetic 
flux. In this case the density of vortices is highly inhomogeneous and the flux density can be 
considerably lower than the assumed equilibrium value B/φ0, as the model calculations of this work 
also indicate. For instance, at low fields B < Bs, the density of vortices is mostly controlled by the 
dynamics of their penetration through edge defects rather than by the applied field B. The analysis of 
the experimental data based on the Bezuglyj-Shklovskij model likely underestimates the maximum 
velocities of vortices, which can also affect the values of superconducting parameters, particularly, the 
inelastic scattering times and the LO critical velocity extracted from the fits. These issues, particularly 
the role of edge defects, should be discussed. 
4. Such important parameters of Nb-C as λ and ξ should be specified on pp 4 and 5, and the Pearl 
length λ^2/d be calculated explicitly and compared with the width of the film where it was first 
mentioned but not at the end of the paper around Table 1. 
5. The description of the theoretical model in methods is not very informative and its relevance to the 
experimental part was not made clear. For instance, it was not explained why the TDGL eqs on p. 25 
lack the inelastic scattering time constant which plays such an important role in the analysis of the 
experimental data based on the LO mechanism in the main text. Also the undefined expression div 
(j^Us-j^GL} is confusing, suggesting that the GL current somehow does not follow from the Usadel 
theory near Tc. Given a potentially diverse scientific readership of Nature Communication outside the 
photon detector community, it would be more appropriate to replace the cryptic div (j^Us-j^GL} with 
an explicit expression which readily follows from Eqs. 33 and 34 of Ref. 51. 


Reviewer #2 (Remarks to the Author): 

The work "Ultra-fast vortex motion in dirty Nb-C superconductor with a close-to-perfect edge barrier" 
by Dobrovolskiy et al. presents indirect experiment evidence of ultra-fast vortices in a Nb-C 
superconductor dominated by edge barrier. The theoretical analysis is based on a previous publication 
of one of the authors (Ref.[33]). 

The paper is well written and structured, interesting, and scientifically sound. Although it certainly 
contains a good level of originality (sample fabrication, material, LLI in edge barrier dominated 
samples) and it deserves publication in some form, I consider that it does not really present 
sufficiently exciting results or will influence thinking in the field. 

In addition, I believe the case presented in this manuscript would be reinforced if the results were 
compared with those obtained in a sample with roughness along its border so as to diminish the 
influence of the edge barriers. For instance introducing a small notch at the surface will reduce Bs. 

The text is easy to read but here and there the English can be polished.