  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.
