Unified formalism for calculating polarization, magnetization, and more in a periodic insulator
Name
Chen-2011-Unified formalism for calculating polarization, magnetization.pdf
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271.52 KB
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Author(s)
Chen, Kuang-Ting
Lee, Patrick A.
Date Issued
November 2011
Journal
Physical Review B
Publisher
American Physical Society
Citation
Chen, Kuang-Ting, and Patrick Lee. “Unified Formalism for Calculating Polarization, Magnetization, and More in a Periodic Insulator.” Physical Review B 84.20 (2011):[14 pages]. ©2011 American Physical Society.
Version
Final published version
Abstract
In this paper, we propose a unified formalism, using Green's functions, to integrate out the electrons in an insulator under uniform electromagnetic fields. We derive a perturbative formula for the Green's function in the presence of uniform magnetic or electric fields. By applying the formula, we derive the formula for the polarization, the orbital magnetization, and the orbital magnetopolarizability, without assuming time-reversal symmetry. Specifically, we realize that the terms linear in the electric field can only be expressed in terms of the Green's functions in one extra dimension. This observation directly leads to the result that the coefficient of the θ term in any dimensions is given by a Wess-Zumino-Witten–type term, integrated in the extended space, interpolating between the original physical Brillouin zone and a trivial system, with the group element replaced by the Green's function. This generalizes an earlier result for the case of time-reversal invariance [see Z. Wang, X.-L. Qi and S.-C. Zhang Phys. Rev. Lett. 105 256803 (2010)].
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.84.205137
