Half-quantized Hall effect and power law decay of edge-current distribution

Abstract

Half-quantized Hall conductance is characteristic of quantum systems with the 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 uncover a distinct bulk-edge correspondence in which 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 according to a power law instead of an exponential law in the integer quantum Hall effect. We further address the physical relevance of parity anomalous semimetals to three-dimensional semimagnetic topological insulators and two-dimensional photonic crystals.