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Precise quantum-geometric electronic properties from first principles
by José Luís Martins, Carlos Loia Reis, Ivo Souza
Submission summary
| Authors (as registered SciPost users): | José Luís Martins · Ivo Souza |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2506.23652v2 (pdf) |
| Code repository: | https://github.com/jlm785/cpw2000 |
| Date accepted: | Oct. 6, 2025 |
| Date submitted: | Sept. 3, 2025, 12:20 p.m. |
| Submitted by: | José Luís Martins |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The calculation of quantum-geometric properties of Bloch electrons -- Berry curvature, quantum metric, orbital magnetic moment and effective mass -- was implemented in a pseudopotential plane-wave code. The starting point was the first derivative of the periodic part of the wavefunction psi_k with respect to the wavevector k. This was evaluated with perturbation theory by solving a Sternheimer equation. Comparison of effective masses obtained from perturbation theory for silicon and gallium arsenide with carefully-converged numerical second derivatives of band energies confirms the high precision of the method. Calculations of quantum-geometric quantities for gapped graphene were performed by adding a bespoke symmetry-breaking potential to first-principles graphene. As the two bands near the opened gap are reasonably isolated, the results could be compared with those obtained from an analytical two-band model, allowing to assess the strengths and limitations of such widely-used models. The final application was trigonal tellurium, where quantum-geometric quantities flip sign with chirality.
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Author comments upon resubmission
List of changes
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List of additional changes not mentioned in the Author Replies
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As suggested by the Editor, we have added a footnote on p. 1 mentioning that our co-author Carlos L. Reis passed away before the work was concluded.
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Added a new reference (Ref. 4), cited in the Introduction (p.2 line 22).
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Replaced the symbol $v_{\rm eff}$ with $V_{\rm eff}$ for the effective potential throughout the manuscript.
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Stated that the normalization volume is one crystal cell and that the atomic units are Hartree. (p.3 line 75)
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Removed the acronym "mBJ" for the "modified Becke-Johnson" meta-GGA functional. (line 320)
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In the text we corrected "(in units of 2.pi/a)" to "(in atomic units)", Caption of Table I was correct. (p. 10 line 280)
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In equations 38 to 43 of the low energy model we made the appearence consistent with a explicit dependence on q_x and q_y = 0. Before some equations had the (correct) dependence on q = sqrt(q_x^2+q_y^2). The consistency should help the reader.
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Below Eqs. (42) and (43), it is now mentioned that a factor of 1/a_0^2 E_H is omitted, since it is equal to one in atomic units. This dispells any possible confusion about the units. (p. 19)
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In the caption of Fig. 8, the relevant equation [Eq. (44)] is now mentioned at the beginning. (p. 21)
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In the first paragraph of the Conclusions, a sentence was added at the end about the intraband contribution to the inverse effective-mass tensor. (p. 27 lines 598-600)
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Made the title of Ref. [40] (line 735) more descriptive. It now reads "Pseudopotential generation code".
In some places, minor changes have been made to the wording to improve the clarity of presentation. These very minor changes are not listed.
Published as SciPost Phys. 19, 109 (2025)
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