  We propose that half-quantized helical hinge currents manifest as the
fingerprint of the axion insulator (AI). These helical hinge currents
microscopically originate from the lateral Goos-H\"anchen (GH) shift of
massless side-surface Dirac electrons that are totally reflected from the
hinges. Meanwhile, due to the presence of the massive top and bottom surfaces
of the AI, the helical current induced by the GH shift is half-quantized. The
semiclassical wave packet analysis uncovers that the hinge current has a
topological origin and its half-quantization is robust to parameter changes.
Lastly, we propose an experimentally feasible six-terminal device to identify
the half-quantized hinge channels by measuring the nonreciprocal conductances.
Our results advance the understanding of the non-trivial transport and
topological magnetoelectric responses in AIs.
