Theory of orbital magnetoelectric response
Open accessAbstract
We extend the recently developed theory of bulk orbital magnetization to finite electric fields, and use it to calculate the orbital magnetoelectric (ME) response of periodic insulators. Working in the independent-particle framework, we find that the finite-field orbital magnetization can be written as a sum of three gauge-invariant contributions, one of which has no counterpart at zero field. The extra contribution is collinear with and explicitly dependent on the electric field. The expression for the orbital magnetization is suitable for first-principles implementations, allowing one to calculate the ME response coefficients by numerical differentiation. Alternatively, perturbation-theory techniques may be used, and for that purpose we derive an expression directly for the linear ME tensor by taking the first field-derivative analytically. Two types of terms are obtained. One, the 'Chern–Simons' term, depends only on the unperturbed occupied orbitals and is purely isotropic. The other, 'Kubo' terms, involve the first-order change in the orbitals and give isotropic as well as anisotropic contributions to the response. In ordinary ME insulators all terms are generally present, while in strong Z 2 topological insulators only the Chern–Simons term is allowed, and is quantized. In order to validate the theory, we have calculated under periodic boundary conditions the linear ME susceptibility for a 3D tight-binding model of an ordinary ME insulator, using both the finite-field and perturbation-theory expressions. The results are in excellent agreement with calculations on bounded samples.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In general, the orbital magnetoelectric polarizability of a 3D crystal, even its diagonal part, contains further terms beyond the Berry phase.
“in general the orbital magnetoelectric polarizability of a 3D crystal, even its diagonal part, contains further terms beyond the Berry phase (the correct expression is in (72,80))”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [80]
For a general solid, not necessarily a topological insulator, the Chern-Simons integral is just one contribution to the electromagnetic θ.
“The improvement is that these make clear that, for a general solid (not necessarily a topological insulator), the Chern-Simons integral is just one contribution to the electromagnetic θ .”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [80]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
The citation lists haven’t been fetched yet
References 40 · Cited by 160
- Authors
- Malashevich, A., Souza, I., Coh, S., & Vanderbilt, D.
- Affiliations
- University of California, Berkeley (US)
- Rutgers, The State University of New Jersey (US)
- Corresponding author
- Coh, Sinisa
- Venue
- New Journal of Physics
- Publisher
- IOP Publishing
- Published
- 2010-05-21
- Volume
- 12
- Issue
- 5
- Pages
- 053032
- ISSN
- 1367-2630 (ISSN-L)
- OpenAlex
- W2157180835
- Cited by
- 160
- References
- 40
- Citations by year
- 2026: 11 · 2025: 5 · 2024: 6 · 2023: 14 · 2022: 9 · 2021: 18 · 2020: 10 · 2019: 9 · 2018: 18 · 2017: 9 · 2016: 6 · 2015: 9 · 2014: 6 · 2013: 5 · 2012: 11
- FWCI
- 5.15
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- cc-by
- Locations
- New Journal of Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0706493, 0549198)
- National Energy Research Scientific Computing Center
- Division of Materials Research
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Multiferroics and related materials
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- orbital magnetization, finite electric field, Chern-Simons term, Z2 topological insulator, tight-binding model, first-principles calculations
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
