  A three-dimensional topological insulator features a two-dimensional surface
state consisting of a single linearly-dispersive Dirac cone. 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. However, despite various observations
of quantization phenomena, the half-integer quantization has been elusive
because a pair of equivalent Dirac cones on two opposing surfaces are
simultaneously measured in ordinary experiments. 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/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
and open a way for studying unconventional physics enabled by a single Dirac
fermion.
