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Tunable second harmonic generation in 2D materials: comparison of different strategies
by Simone Grillo, Elena Cannuccia, Maurizia Palummo, Olivia Pulci, Claudio Attaccalite
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Claudio Attaccalite |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202410_00031v1 (pdf) |
| Date submitted: | 2024-10-14 14:03 |
| Submitted by: | Attaccalite, Claudio |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Nonlinear optical frequency conversion, where optical fields interact with a non-linear medium to generate new frequencies, is a key phenomenon in modern photonic systems. However, a major challenge with these techniques lies on the difficulty of tuning the nonlinear electrical susceptibilities that drive such effects in a given material. As a result, dynamic control of optical nonlinearities has remained largely confined to research laboratories, limiting its practical use as a spectroscopic tool. In this work, we aim to advance the development of devices with tunable nonlinear responses by exploring two potential mechanisms for electrically manipulating second-order optical nonlinearity in two-dimensional materials. Specifically, we consider two configurations: in the first, the material does not inherently exhibit second-harmonic generation (SHG), but this response is induced by an external field; in the second, an external field induces doping in a material that already exhibits SHG, altering the intensity of the nonlinear signal. These two approaches are investigated and compared with existing experimental results.
Current status:
Reports on this Submission
Report
The authors perform first-principles calculations on the second-harmonic
generation in bilayer MoS_2 exposed to an electric field and
doped monolayer WSe_2. Notably, an approximation is used to include
electron-hole attraction effects that are typically neglected.
Interestingly, it is shown that the SHG enhancement in 2D systems due electric fields
is essentially related to electronic structure modifications, while the
ionic contributions are minor.
The results are original, interesting and well presented. They will be of
interest to the community. I suggest publication of the manuscript as is.
Recommendation
Publish (meets expectations and criteria for this Journal)
Strengths
I have read the manuscript "Tunable second harmonic generation in 2D materials: comparison of different strategies" and, overall, I find it interesting and timely in the field of 2D materials. It presents the results of computer calculations of the non-linear (second order) susceptibility for mono- and bilayer transition metal dichalcogenides. The results provide possible routes to control the second harmonic generation in such materials.
Weaknesses
I see no significant weaknesses of the work. A minor point here is the lack of simple analytical models (that could clarify the origin of SHG, e.g., along the lines of Phys. Rev. B 95, 035311 (2017)).
Report
Overall, the manuscript is suitable for the SciPost Physics Core journal provided the authors make the requested changes, see below.
Requested changes
1.A comment regarding the validity of the "coordinate" gauge (E\cdot \partial/\partial k) is needed. In particular, the coordinate operator in the crystals contains, apart from the `i \partial/\partial k' contribution a part \Omega related to the Berry curvature of the bands.
2. The authors should clarify the origin of the resonance in \chi at 2\omega \approx 0.8..0.85 eV in monolayer WSe_2 (Fig. 3). I am unaware about any resonances in optical response of monolayers in this range. Possible, \omega \approx 0.8..0.85 eV and 2\omega \approx 1.6 .. 1.7 eV which is close to the excitonic resonances.
Recommendation
Ask for minor revision
Author: Claudio Attaccalite on 2024-11-07 [id 4943]
(in reply to Report 2 on 2024-10-30)
Errors in user-supplied markup (flagged; corrections coming soon)
We thank the referees for their positive feedback. Below, we provide our responses to the specific points raised by both referees and address additional comments on our manuscript:
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> Revisit the abstract. Title and abstract describe the setting, but not what has actually been done.
> At least one sentence should be added that reflects section 2 ("Theoretical Methods") of the manuscript.
In the revised version of the manuscript, we have updated the abstract to clearly describe the theoretical methods employed.
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> Add DOIs to all references where they are available (these are "particularly important," see https://scipost.org/SciPostPhysCore/authoring#manuprep).
We have proceeded to add DOIs to all applicable references.
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> Proofread titles of references, e.g., "MoS2" [7-10], "h-BN" [7], "ReS2 [11], "WSe2 [13], "GW" [16,31], "Berry" [17,18], "Bethe-Salpeter" [20,28], "Wannier" [28], "Mott" [32], "Si" [32], "Al0.7Ga0.3N" [32], and "Fröhlich" [37].
We have thoroughly proofread and corrected all reference titles to ensure accuracy and consistency.
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> A comment regarding the validity of the "coordinate" gauge (\( E \cdot \partial/\partial k \)) is needed. Specifically, the coordinate operator in crystals includes, apart from the \( i \partial/\partial k \) contribution, a term \( \Omega \) related to the Berry curvature of the bands.
We have included a sentence in the revised manuscript that explains the validity of the k-derivative of the time-dependent valence bands and its relation to the generalized Berry connection in the standard crystal momentum representation.
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> The authors should clarify the origin of the resonance in \(\chi\) at \(2\omega \approx 0.8-0.85\) eV in monolayer WSe\(_2\) (Fig. 3). I am not aware of any resonances in the optical response of monolayers in this range. Possibly, \(\omega \approx 0.8-0.85\) eV corresponds to \(2\omega \approx 1.6-1.7\) eV, which is close to excitonic resonances.
We have added a sentence explaining that the observed resonance at 0.8 eV corresponds to half the energy of the A exciton at 1.65 eV. This exciton has been confirmed in several experimental and theoretical studies. We have also added a reference where this resonance is discussed and compared with experimental data.
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> I see no significant weaknesses in the work. A minor point is the lack of simple analytical models (that could clarify the origin of SHG, e.g., along the lines of Phys. Rev. B 95, 035311 (2017)).
We appreciate this observation. While finalizing our manuscript, we noted the recent publication of a simplified model for nonlinear response in gated bilayer graphene in PRB. This model incorporates many of the physical effects addressed in our paper, albeit within a simpler framework than that of dichalcogenides. We have added a citation to this work in our manuscript.
Anonymous on 2024-10-29 [id 4910]
Thank you for this comment we will fix the references and improve the abstract in the new version of the manuscript.
Anonymous on 2024-10-29 [id 4909]
1- Revisit the abstract. Title and abstract describe the setting, but not what has actually been done. At least one sentence should be added that reflects section 2 ("Theoretical Methods") of the manuscript. 2- Add DOIs to all references where they are available (these are "particularly important", see https://scipost.org/SciPostPhysCore/authoring#manuprep). 3- Proofread titles of references, e.g.: "MoS$_2$" [7-10], "h-BN" [7], "ReS$_2$ [11], "WSe$_2$ [13], "GW" [16,31], "Berry" [17,18], "Bethe-Salpeter" [20,28], "Wannier" [28], "Mott" [32], "Si" [32], "Al$_{0.7}$ Ga$_{0.3}$N" [32], and "Fröhlich" [37].