Non-Hermitian effect to the ballistic transport and quantized Hall conductivity in 2H-MoS$_{2}$

By designing a multi-channel millimeter Hall measurement configuration, we realize the carrier-density (locally) controllable measurement on the transport property in 2H MoS$_{2}$. We observe a linearly increased Hall conductivity and exponentially decreased resistivity as the increase of dc current. The intrinsically large band gap does not exhibit too much effect on our measurement, as far as the magnetic field is above the critical value, which is $B=6$ T for 2H-MoS$_{2}$. Instead, the edge effect which emerge as a result of one-dimensional channels. This is different from the Corbino geometry which is widely applied on semiconductors, where the edges are absent. At room temperature, we observe that the emergent quantized quantum Hall plateaus are at the same value for both the two measurements, which implies that the quantized conductivity does not depends on the non-Hermitian interactions, but the number of partially filled Landau levels, and this is in consistent with the previous theoretical works\cite{Siddiki}. At low-temperature limit, the Hall plateaus are destroyed due to the filtered contribution from the electrons above fermi energy, and in this case, the two measuremens exhibits stronger distinction, where we observe stronger fluctuations (of voltage, conductivity, and resistivity) at the currents between where there are Hall plateaus at higher temperature.