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DFT2kp: effective kp models from ab-initio data
by João Victor V. Cassiano, Augusto L. Araújo, Paulo E. Faria Junior, Gerson J. Ferreira
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Paulo E. Faria Junior · Gerson J. Ferreira · Augusto de Lelis Araújo |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202312_00029v1 (pdf) |
| Code repository: | https://gitlab.com/dft2kp/dft2kp |
| Date accepted: | 2024-01-10 |
| Date submitted: | 2023-12-15 20:30 |
| Submitted by: | J. Ferreira, Gerson |
| Submitted to: | SciPost Physics Codebases |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The $\bm{k}\cdot\bm{p}$ method, combined with group theory, is an efficient approach to obtain the low energy effective Hamiltonians of crystalline materials. Although the Hamiltonian coefficients are written as matrix elements of the generalized momentum operator $\bm{\pi}=\bm{p}+\bm{p}_{{\rm SOC}}$ (including spin-orbit coupling corrections), their numerical values must be determined from outside sources, such as experiments or \emph{ab initio} methods. Here, we develop a code to explicitly calculate the Kane (linear in crystal momentum) and Luttinger (quadratic in crystal momentum) parameters of $\bm{k}\cdot\bm{p}$ effective Hamiltonians directly from \emph{ab initio} wave-functions provided by Quantum ESPRESSO. Additionally, the code analyzes the symmetry transformations of the wave-functions to optimize the final Hamiltonian. This an optional step in the code, where it numerically finds the unitary transformation $U$ that rotates the basis towards an optimal symmetry-adapted representation informed by the user. Throughout the paper we present the methodology in detail, and illustrate the capabilities of the code applying it to a selection of relevant materials. Particularly, we show a ``hands on'' example on how to run the code for graphene (with and without spin-orbit coupling). The code is open source and available at \href{https://gitlab.com/dft2kp/dft2kp}{https://gitlab.com/dft2kp/dft2kp}.
Author comments upon resubmission
We are thankful for insightful reports from both referees. The questions raised in this reports helped us identify weakness in our discussions and to significantly improve the manuscript. Both referees reports were overall positive. Particularly, the second referee explicitly suggests that SciPost Physics Codebase is the appropriate Journal for our manuscript, and the first referee does give an explicit position, but report implies that the referee is willing to accept the paper for publication after the requested revisions.
In this new version of the manuscript and replies to the referees, we consider all questions raised by the referee in detail. We attached a PDF version of the manuscript highlighting all changes since the original version. We believe that this version was significantly improved by the peer-review process and we hope that it is ready for publication in SciPost Physics Codebases.
Yours Sincerely,
The authors
List of changes
Here we summarize the most relevant changes in this new version of the manuscript. Additionally, the reply to the referees present other minor changes that help to answer the questions in their reports. Other minor changes of style and corrections found during the revison of the text can be seen in the diff.pdf file attached to this resubmission, which uses latexdiff to mark all deletions in strikethrough-red and additions in blue.
List of changes:
TO DO: mention the referee requests on each item.
(1) Abstract.
Referee 2: requests 1 and 2
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A sentence regarding the fitting of DFT data was improved to match the new text detailed in item (2) below.
(2) Introduction, 4th paragraph.
Referee 2: requests 1 and 2
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Improved discussion on how kp parameters are usually obtained by either fiting DFT data, or by comparing predictions to experimental measurements. Additionally, at the end of this paragraph we change our sentence about the Wannier90 code to correctly describe its functionality. We have also added references suggested by the referees.
(3) Section II.C, second paragraph.
Referee 1: weakness 1 and request 10
Referee 2: request 3
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Improved discussion on the comparison between our new method to find the transformation matrix U between reducible representations and the method from Mozrzymas et al.
(3) Section II.C, last two paragraph.
Referee 2: request 4
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New discussion on the uniquenes of the transformation matrix U and the relative phases between irreps. T
(4) Section III.C
Referee 1: weakness 1 and request 10
Referee 2: request 3
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New section with the spinful graphene example to illustrate the case of reducible representations.
(5) Section IV.B.1
Referee 1: weakness 2 and request 11
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New section showing a comparison of GaN and GaP results calculated with and wihtout the SOC/PAW corrections to the Pmn matrix element.
(6) Section V.A
Referee 1: request 8
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The new version of Fig. 8 (previous Fig. 6) adds a measurement of convergence based on the discrete derivative of the coefficients as a function of the number of bands. The text was edited to present this new figure.
(7) Conclusions
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Adding a citation to a recently develop code VASP2kp that is similar to ours, but works on VASP instead of QE.
Published as SciPost Phys. Codebases 25 (2024) , SciPost Phys. Codebases 25-r0.0 (2024)