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Multipole theory of optical spatial dispersion in crystals
by Óscar Pozo Ocaña and Ivo Souza
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Submission summary
| Authors (as registered SciPost users): | Óscar Pozo Ocaña · Ivo Souza |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202212_00003v2 (pdf) |
| Date submitted: | 2023-02-23 17:39 |
| Submitted by: | Pozo Ocaña, Óscar |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Natural optical activity is the paradigmatic example of an effect originating in the weak spatial inhomogeneity of the electromagnetic field on the atomic scale. In molecules, such effects are well described by the multipole theory of electromagnetism, where the coupling to light is treated semiclassically beyond the electric-dipole approximation. That theory has two shortcomings: it is limited to bounded systems, and its building blocks - the multipole transition moments - are origin dependent. In this work, we recast the multipole theory in a translationally-invariant form that remains valid for crystals. Working in the independent-particle approximation, we introduce "intrinsic" multipole transition moments that are origin independent and transform covariantly under gauge transformations of the Bloch eigenstates. Electric-dipole transitions are given by the interband Berry connection, while magnetic-dipole and electric-quadrupole transitions are described by matrix generalizations of the intrinsic magnetic moment and quantum metric. In addition to multipole-like terms, the response of crystals at first order in the wavevector of light contains band-dispersion terms that have no counterpart in molecular theories. The full response is broken down into magnetoelectric and quadrupolar parts, which can be isolated in the static limit where electric and magnetic fields become decoupled. The rotatory-strength sum rule for crystals is found to be equivalent to the topological constraint for a vanishing chiral magnetic effect in equilibrium, and the formalism is validated by numerical tight-binding calculations.
List of changes
- Added a new section (Sec. 3.6), and made corresponding changes in the Introduction and Summary sections.
- The titles of Secs. 3, 3.1, 3.2, 3.3, 3.5.1, and 3.5.2 have been reworded for clarity.
- Added, at the end of Sec. 2 and beginning of Sec. 3.5, a discussion of the restrictions imposed on the spatially-dispersive conductivity by inversion (P), time reversal (T), and by the combined PT symmetry.
- Some reorganization around Eqs.(11,12), which made the text shorter.
- Factorized an expression in Eq. (14d).
- Dropped an incorrect sentence below Eq. (27).
- Dropped a sentence below Eq. (32).
- A (formally vanishing) term was added to Eq. (47) for clarity.
- Corrected a typo in the second term of Eq.(57).
- Made some changes in Fig. 1(a) (right side), and added an explanatory sentence in the caption.
- Dropped a sentence below Eq. (58).
- Dropped from Sec. 6 a speculative discussion about future prospect for numerical calculations on conducting crystallites.
- Fixed the labels of the dashed curves in Fig. 4 (they were swapped).
- Shortened the "Summary and discussion" section.
- Added several new references, and removed a few.
- Fixed several typos throughout the manuscript, and made changes in wording at various places to improve the clarity of the text.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 5) on 2023-3-2 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202212_00003v2, delivered 2023-03-02, doi: 10.21468/SciPost.Report.6835
Report
The authors have provided satisfactory answers to my questions, and I am generally happy with the revision of the text. There is only one sentence that caught my attention, and should probably be fixed: at page 6 "similar comments apply to first-principles calculations using nonlocal pseudopotentials." What do the authors mean here? A theory of the current-density response in presence of nonlocal pseudos was presented in
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.98.075153
This work seems to suggest that even Eq.(6) of the present manuscript should be revised in presence of nonlocal pseudos. Is this what the authors meant with their comment? It might be worth rewording it, as it sounds ambiguous in the present form. While I do recommend such a revision, I leave it to the discretion of the authors.
Author: Óscar Pozo Ocaña on 2023-03-06 [id 3443]
(in reply to Report 2 on 2023-03-02)We thank the referee for raising the issue of nonlocal pseudopotentials, and for providing the very useful reference. In view of that work, we feel that this issue needs to be investigated further. For the purpose of the present work, where only tight-binding calculations are presented, the sentence about nonlocal pseudopotentials can be safely removed. We have done so in the resubmitted manuscript, and we now mention above Eq. (6) that a local external potential is assumed.
Anonymous on 2023-02-27 [id 3407]
I confirm my previous positive review after the changes implemented by the authors