Quantum Anomalous Hall Effect & Axion Electrodynamics

A magnetically doped topological insulator exhibits quantized Hall conductance σ_xy = (e²/h)·C without an external field. The axion term θ=π encodes topological magnetoelectric coupling.

Axion term: ℒ_θ = (θα/4π²) E·B
θ = π → topological insulator
θ = 0 → trivial insulator
Hall conductance: σ_xy = Ce²/h
Edge modes: |C| chiral channels