Unified Formalism for calculating Polarization, Magnetization, and more in a Periodic Insulator

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. Applying the formula, we derive the formula for the polarization, the orbital magnetization, and the orbital magneto-polarizability, 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. {\bf 105}, 256803 (2010)].

16 pages, 1 figure. The version accepted by PRB

References in corpus (7)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Orbital magnetization in periodic insulators
• Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems
• Theory of orbital magnetoelectric response
• Dichroic f-sum rule and the orbital magnetization of crystals
• Density-operator theory of orbital magnetic susceptibility in periodic insulators
• Hall Coefficient in an Interacting Electron Gas

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