Dissipative chiral channels, Ohmic scaling, and half-integer Hall conductivity from relativistic quantum Hall effect

The quantum Hall effect, which was observed in two-dimensional (2D) electron gases 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 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 between 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 three-dimensional topological insulators to directly measure the HIHC. Our findings not only uncover the distinct transport mechanism of the HIHC for the RQHE but also pave the way for the measurement of the HIHC in future experiments.