Half Quantum Mirror Hall Effect

Abstract

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.