Orbital magnetoelectric coupling in band insulators
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Magnetoelectric responses are a fundamental characteristic of materials that break time-reversal and inversion symmetries (notably multiferroics) and, remarkably, of ``topological insulators'' in which those symmetries are unbroken. Previous work has shown how to compute spin and lattice contributions to the magnetoelectric tensor. Here we solve the problem of orbital contributions by computing the frozen-lattice electronic polarization induced by a magnetic field. One part of this response (the ``Chern-Simons term'') can appear even in time-reversal-symmetric materials and has been previously shown to be quantized in topological insulators. In general materials there are additional orbital contributions to all parts of the magnetoelectric tensor; these vanish in topological insulators by symmetry and also vanish in several simplified models without time reversal and inversion whose magnetoelectric couplings were studied before. We give two derivations of the response formula, one based on a uniform magnetic field and one based on extrapolation of a long-wavelength magnetic field, and discuss some of the consequences of this formula.
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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 [72]
The three-dimensional topological insulator is connected to the orbital contribution to the magnetoelectric polarizability dP/dB.
“The three-dimensional topological insulator turns out to be connected to a basic electromagnetic property of solids: the orbital contribution to the magnetoelectric polarizability dP/dB (70,71,72).”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [72]
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 [72]
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References 30 · Cited by 193
Research works printed but not linked: 1
- 29 P. A. M. Dirac, Proc. Cam. Phil. Soc. 27 , 240 (1931), in The collected works of P. A. M. Dirac, 1924-1928 , ed. R. H. Dalitz, Cambridge University Press (1995).
- Authors
- Essin, A. M., Turner, A. M., Moore, J. E., & Vanderbilt, D.
- Affiliations
- University of California, Berkeley (US)
- Lawrence Berkeley National Laboratory (US)
- Rutgers, The State University of New Jersey (US)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2010-05-06
- Volume
- 81
- Issue
- 20
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2117830338
- Cited by
- 193
- References
- 30
- Citations by year
- 2026: 6 · 2025: 10 · 2024: 6 · 2023: 12 · 2022: 8 · 2021: 14 · 2020: 10 · 2019: 16 · 2018: 22 · 2017: 13 · 2016: 9 · 2015: 12 · 2014: 11 · 2013: 10 · 2012: 11
- FWCI
- 7.55
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- 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
- magnetoelectric tensor, band insulator, topological insulators, Chern-Simons term, electronic polarization, time-reversal symmetry, inversion symmetry, multiferroics
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