  The quantum Hall effect (QHE), which was observed in 2D electron gas under an
external magnetic field, stands out as one of the most remarkable transport
phenomena in condensed matter. However, a long standing puzzle remains
regarding the observation of the relativistic quantum Hall effect (RQHE). This
effect, predicted for a single 2D Dirac cone immersed in a magnetic field, is
distinguished by the intriguing feature of half-integer Hall conductivity
(HIHC). In this work, we demonstrate that the condensed-matter realization of
the RQHE and the direct measurement of the HIHC are feasible by investigating
the underlying quantum transport mechanism. We reveal that the manifestation of
HIHC is tied to the presence of dissipative half-integer quantized chiral
channels circulating along the interface of the RQHE system and a Dirac metal.
Importantly, we find that the Ohmic scaling of the longitudinal conductance of
the system plays a key role in directly measuring the HIHC in experiments.
Furthermore, we propose a feasible experimental scheme based on the 3D
topological insulators to directly measure the HIHC. Our findings not only
uncover the distinct transport mechanism of the HIHC for the RQHE, but also
paves the way to the measurement of the HIHC in future experiments.
