Experimental signature of the parity anomaly in a semi-magnetic topological insulator

A three-dimensional (3D) topological insulator features a 2D surface state consisting of a single linearly dispersive Dirac cone^1–3. Under broken time-reversal symmetry, the single Dirac cone is predicted to cause half-integer quantization of Hall conductance, which is a manifestation of the parity anomaly in quantum field theory^1–9. However, despite various observations of quantization phenomena^10–15, the half-integer quantization has not been observed because most experiments simultaneously measure a pair of equivalent Dirac cones¹⁶ on two opposing surfaces. Here we demonstrate the half-integer quantization of Hall conductance in a synthetic heterostructure termed a semi-magnetic topological insulator, where only one surface state is gapped by magnetic doping and the opposite one is non-magnetic and gapless. We observe half-quantized Faraday and Kerr rotations with terahertz magneto-optical spectroscopy and half-quantized Hall conductance in transport at zero magnetic field. Our results suggest a condensed-matter realization of the parity anomaly^4–9 and open a way for studying the physics enabled by a single Dirac fermion.