Peer review of: Non-perturbative terahertz high-harmonic generation in the three-dimensional Dirac semimetal C (2020)

Reviewers' comments: 

Reviewer #1 (Remarks to the Author): 

The paper describes interesting experiments on HHG in the Dirac semimetal Cd3As2. I am in favor 
of acceptance of the paper provided the following changes have been made prior to publication. 

I regard as mandatory: 
1. The authors use an extremely simple quasi-classical model basically without any quantum 
mechanics to describe the obtained results. It is surprising and it is to my opinion an important 
result of the paper that this model can at least qualitatively reproduce the experimental findings 
for moderate intensities. The authors should more clearly underline the simplifications of their 
model and avoid statements as “the analysis is performed without further assumptions”. 
2. I would like to see a statement on the role of the Fermi energy in the main paper. If the model 
is correct its position must be crucial for HHG. I can understand that a variation of that parameter 
might not be accessible in the experiment, but respective simulations should be performed and 
discussed in the supplementary. 
2. Unless I have overlooked it, but the authors should give the power dependence for the different 
harmonics displayed in Figs 3 c-e (represented by bold lines). 
Optionally I recommend the authors to look for a simple explanation for the observed power law 
dependence of the different harmonics on the driving pump intensity. The paper would gain a lot 
by such an explanation. However, it might be that there is no simple explanation. 



Reviewer #2 (Remarks to the Author): 

Reports Kovalev et al. 
Non-perturbative terahertz high-harmonic generation in the three^dimensional Dirac semimetal 
Cd3As2 

This communication reports the THz high-harmonic generation based on both experiment and 
theoretical analysis. The experiments are performed using THz pump light (0.7 THz and 0.3 THz) 
and EO sampling to detect time evolutions of the emitted electric field of the HHG up to 7-th 
order(for 0.3 THz pump). The authors analyze the nonlinear-transient current reflecting electron 
distribution function t(t, p) using the Boltzmann transport theory. The authors claim that the THz 
HHG in Ca3As2 is well described by non-equilibrium intra-band charge distribution. They also claim 
that the observed excitation intensity dependence (which is smaller than those for perturbative 
power low) is reproducible by the above analysis, indicating the non-perturbative mechanism of 
the HHG in the Dirac system. 
They nicely achieve the observations of the HHG up to 7-th order HHG as real time waveforms 
using 0.3 THz pump light from a linear electron accelerator which is accurately synchronized with a 
femtosecond laser. In addition, the real time tracking of the distribution of f(t, p) in the analysis, 
demonstrating the asymmetric stretching of the electronic distribution toward the direction of the 
applied THz field (and the resultant flat-peak like feature in the time profile of the current density 
profile), is very clear to see that the HHG is driven by such non-equilibrium intra-band charge 
distribution. I agree that, the HHG is successfully in the Dirac electron having a linear dispersion 
relation). 
Another important issues of this manuscript is that they could determine the intra-band relaxation 
time (in the Boltzmann theory) for reproducing the fullerene dependence. They denote that 
"Furthermore, we found that efficiency and fluence-dependence of the THz HHG is very sensitive to 
the scattering rate 1/tau ". That is very important for clarifying the mechanism of HHG in Dirac 
and Weyl system. 
Considering the attracting features of the 3D Dirac and Weyl materials and their possible nonlinear 
photonics, I agree the THz HHG of this typical Dirac compound can provide large impact both in 
the solid-state physics and the photonics communities. Therefore, I recommend publication of this 
paper. However, while I have no doubts on the very important observations of the HHG and their 
analysis, I have a few tiny comments and queries (most of them are techncal problems). 

i) Why do you use asymmetric electric field in the calculation (Fig. 2(a)) ?. That is different from 
the THz pulse used in the experiment (Fig. 3(b)). 

ii) I think that more detailed discussions can be useful for the intra-band relaxation time. Is it 
possible to consider the microscopic mechanism of the scattering ? The scattering time of 10 fs is 
likely to be reasonable (as actually shown in graphene (ref 43)). However, I'm not sure that it is 
really justified also in this compound. 

iii) It seems not so clear that the fluence dependence (in the analysis ) is sensitive to 1/tau in 
extended data fig.3, although the authors have said so. 

iv) Moreover, I'm also interested in the calculated results for stronger field (such as several MV/cm 
in the analysis). Is it qualitatively different from those shown here?