Polarization and orbital magnetization in Chern insulators: A microscopic perspective

Abstract

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.

13 pages

References in corpus (8)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Orbital magnetization in periodic insulators
• Wannier representation of Z_2 topological insulators
• Exponential localization of Wannier functions in insulators
• Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems
• Theory of orbital magnetoelectric response
• Electric polarization in a Chern insulator
• Chern and Fu-Kane-Mele invariants as topological obstructions

Cited by in corpus (6)

• Instantaneous response and quantum geometry of insulators
• Electric polarization and magnetization in metals
• Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect
• Multipolar quantum electrodynamics of localized charge-current distributions: Spectral theory and renormalization
• Microscopic Theory of the Magnetic Susceptibility of Insulators
• Chern insulators in two and three dimensions: A global perspective