  We report the discovery of the half-quantized mirror Hall effect, a novel
quantum-anomaly induced by mirror symmetry in a strong topological insulator
(TI) film. These films are known to host a pair of gapless Dirac cones
associated with surface electrons. Our findings reveal that mirror symmetry
assigns a unique mirror parity to each Dirac cone, resulting in a
half-quantized Hall conductance of $\pm\frac{e^{2}}{2h}$ for each cone. Despite
the total electric Hall conductance being null due to time-reversal invariance,
the difference in the Hall conductance between the two cones yields a quantized
Hall conductance of $\frac{e^{2}}{h}$ for the difference in mirror currents.
The effect of helical edge mirror current, a crucial feature of this quantum
effect, can be determined by means of electrical measurements. Overall, the
half-quantum mirror Hall effect reveals a new type of mirror-symmetry induced
quantum anomaly in a time-reversal invariant lattice system, giving rise to a
topological metallic state of matter with time-reversal invariance.
