Magnetoelectric Polarizability and Axion Electrodynamics in Crystalline Insulators
Open accessAbstract
The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $\ensuremath{\theta}$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous materials. This polarizability $\ensuremath{\theta}$ is the same parameter that appears in the ``axion electrodynamics'' Lagrangian $\ensuremath{\Delta}{\mathcal{L}}_{EM}=(\ensuremath{\theta}{e}^{2}/2\ensuremath{\pi}h)\mathbf{E}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{B}$, which is known to describe the unusual magnetoelectric properties of the three-dimensional topological insulator ($\ensuremath{\theta}=\ensuremath{\pi}$). We compute $\ensuremath{\theta}$ for a simple model that accesses the topological insulator and discuss its connection to the surface Hall conductivity. The orbital magnetoelectric polarizability can be generalized to the many-particle wave function and defines the 3D topological insulator, like the integer quantum Hall effect, in terms of a topological ground-state response function.
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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 [71]
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 [71]
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Cites
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Flagged first, then by citations
Research works printed but not linked: 3
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Cited by
Sorted by citations
<i>Colloquium</i> : Topological insulators
Hasan, M. Z., & Kane, C. L. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.3045 · Cited by 19,930 · see citing works
Topological insulators and superconductors
Qi, X.-L., & Zhang, S.-C. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1057 · Cited by 14,394 · see citing works
Berry phase effects on electronic properties
Xiao, D., Chang, M.-C., & Niu, Q. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.1959 · Cited by 5,277 · see citing works
Weyl and Dirac semimetals in three-dimensional solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015001 · Cited by 4,528 · see citing works
“The action is Sθ = 1 2π e2 h ∫ dtdrθ(r, t)E ·B. (21) This is similar to the formalism used in describing the electromagnetic response of topological insulators (Essin et al., 2009; Qi et al., 2008; Wu et al., 2016).”
MethodMaximally localized Wannier functions: Theory and applications
Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I., & Vanderbilt, D. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.1419 · Cited by 3,283 · see citing works
Self-citation<i>Colloquium</i> : Topological band theory
Bansil, A., Lin, H., & Das, T. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.021004 · Cited by 1,587 · see citing works
Benalcazar, W. A., Bernevig, B. A., & Hughes, T. L. (2017) · Physical Review B · doi:10.1103/physrevb.96.245115 · Cited by 1,389 · see citing works
Lin, H., Wray, L. A., Xia, Y., Xu, S., Jia, S., Cava, R. J., Bansil, A., & Hasan, M. Z. (2010) · Nature Materials · doi:10.1038/nmat2771 · Cited by 736 · see citing works
Antiferromagnetic topological insulators
Mong, R. S. K., Essin, A. M., & Moore, J. E. (2010) · Physical Review B · doi:10.1103/physrevb.81.245209 · Cited by 663 · see citing works
Self-citationHedgehog spin texture and Berry’s phase tuning in a magnetic topological insulator
Xu, S.-Y., Neupane, M., Liu, C., Zhang, D., Richardella, A., Andrew Wray, L., Alidoust, N., Leandersson, M., Balasubramanian, T., Sánchez-Barriga, J., et al. (2012) · Nature Physics · doi:10.1038/nphys2351 · Cited by 388 · see citing works
Exciton Condensation and Charge Fractionalization in a Topological Insulator Film
Seradjeh, B., Moore, J. E., & Franz, M. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.066402 · Cited by 267 · see citing works
Self-citationOrbital magnetoelectric coupling in band insulators
Essin, A. M., Turner, A. M., Moore, J. E., & Vanderbilt, D. (2010) · Physical Review B · doi:10.1103/physrevb.81.205104 · Cited by 193 · see citing works
Self-citationMorimoto, T., Zhong, S., Orenstein, J., & Moore, J. E. (2016) · Physical Review B · doi:10.1103/physrevb.94.245121 · Cited by 192 · see citing works
Self-citationTheory of orbital magnetoelectric response
Malashevich, A., Souza, I., Coh, S., & Vanderbilt, D. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/5/053032 · Cited by 160 · see citing works
Self-citationTime-domain terahertz spectroscopy in high magnetic fields
Baydin, A., Makihara, T., Peraca, N. M., & Kono, J. (2021) · Frontiers of Optoelectronics · doi:10.1007/s12200-020-1101-4 · Cited by 34 · see citing works
Weyl and Dirac Semimetals in Three Dimensional Solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2017) · arXiv
“The action is Sθ = 1 2π e2 h ∫ dtdrθ(r, t)E ·B. (21) This is similar to the formalism used in describing the electromagnetic response of topological insulators (Essin et al., 2009; Qi et al., 2008; Wu et al., 2016).”
Method
- Authors
- Essin, 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 Letters
- Publisher
- American Physical Society (APS)
- Published
- 2009-04-10
- Volume
- 102
- Issue
- 14
- Pages
- 146805-146805
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2149260107
- Cited by
- 947
- References
- 4
- Citations by year
- 2026: 47 · 2025: 51 · 2024: 45 · 2023: 61 · 2022: 57 · 2021: 94 · 2020: 67 · 2019: 62 · 2018: 43 · 2017: 42 · 2016: 68 · 2015: 53 · 2014: 43 · 2013: 57 · 2012: 60
- FWCI
- 29.00
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (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 › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Keywords
- axion electrodynamics, topological insulators, crystalline insulators
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