Polarization and orbital magnetization in Chern insulators: A microscopic perspective

We derive macroscopic expressions for the polarization and orbital magnetization of a Chern insulator in its zero-temperature ground state using a previously developed formalism for treating microscopic polarization and magnetization fields in extended media. In the limit of a topologically trivial insulator, our results reduce to those of the modern theories of polarization and magnetization. In a Chern insulator, however, we find a generically nonvanishing microscopic free current density, the macroscopic average of which vanishes. Moreover, the expression that we obtain for the polarization is qualitatively similar to that of the modern theory, while the expressions for the orbital magnetization fundamentally differ; the manner in which they differ elucidates the distinct philosophies of these theoretical frameworks.

Automated summary

In this study, we derive macroscopic expressions for the polarization and orbital magnetization of a Chern insulator at its zero-temperature ground state, using a previously developed formalism for analyzing microscopic polarization and magnetization fields in extended media. Our results demonstrate that, in the case of a topologically trivial insulator, the macroscopic expressions coincide with those of modern theories of polarization and magnetization. However, in the case of a Chern insulator, we observe a generally nonvanishing microscopic free current density, while its macroscopic average is zero. Furthermore, the derived expression for polarization is qualitatively similar to that of the modern theory, whereas the expressions for orbital magnetization differ fundamentally, highlighting the distinctive philosophies of these theoretical frameworks.