  The half-quantized Hall conductance is characteristic of quantum systems with
parity anomaly. Here we investigate topological and transport properties of a
class of parity anomalous semimetals, in which massive Dirac fermions coexist
with massless Dirac fermions in momentum space or real space, and uncovered a
distinct bulk-edge correspondence that the half-quantized Hall effect is
realized via the bulk massless Dirac fermions while the nontrivial Berry
curvature is provided by the massive Dirac fermions. The spatial distribution
of the edge current decays away from the boundary in a power law instead of an
exponential law in integer quantum Hall effect. We further address physical
relevance of parity anomalous semimetal to three-dimensional semi-magnetic
topological insulators and two-dimensional photonic crystals.
