Journal
PHYSICAL REVIEW B
Volume 84, Issue 20, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.84.205137
Keywords
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Funding
- NSF [DMR 1104498]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1104498] Funding Source: National Science Foundation
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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 theta 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)].
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