Polarization and orbital magnetization in Chern insulators: A microscopic perspective
arXiv:2203.05077 · doi:10.1103/PhysRevB.107.115110
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.
arXiv comment13 pages
References in corpus (20)
- Topological Field Theory of Time-Reversal Invariant Insulators
- Maximally localized Wannier functions: Theory and applications
- Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
- Orbital magnetization in periodic insulators
- Wannier representation of Z_2 topological insulators
- Exponential localization of Wannier functions in insulators
- Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals
- Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems
- Twisted equivariant matter
- Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state
- Orbital magnetoelectric coupling in band insulators
- Theory of orbital magnetoelectric response
- Triviality of Bloch and Bloch-Dirac bundles
- Electric polarization in a Chern insulator
- Bloch bundles, Marzari-Vanderbilt functional and maximally localized Wannier functions
- Smooth gauge and Wannier functions for topological band structures in arbitrary dimensions
- Microscopic polarization and magnetization fields in extended systems
- Chern and Fu-Kane-Mele invariants as topological obstructions
- From magnetoelectric response to optical activity
- Magnetoelectric polarizability: A microscopic perspective
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