  Topological insulating states in two-dimensional (2D) materials are ideal
systems to study different types of quantized response signals due to their in
gap metallic states. Very recently, the quantum spin Hall (QSH) effect was
discovered in monolayer $\text{TaIrTe}_4$ via the observation of quantized
longitudinal conductance that rarely exists in other 2D topological insulators.
The non-trivial $Z_2$ topological charges can exist at both charge neutrality
point and the van Hove singularity point with correlation effect induced band
gap. Based on this model 2D material, we studied the switch of quantized
signals between longitudinal conductance and transversal Hall conductance via
tuning external magnetic field. In $Z_2$ topological phase of monolayer
$\text{TaIrTe}_4$, the zero Chern number can be understood as 1-1=0 from the
double band inversion from spin-up and spin-down channels. After applying a
magnetic field perpendicular to the plane, the Zeeman split changes the band
order for one branch of the band inversion from spin-up and spin-down channels,
along with a sign charge of the Berry phase. Then the net Chern number of 1-1=0
is tuned to 1+1=2 or -1-1=-2 depending on the orientation of the magnetic
field. The quantized signal not only provides another effective method for the
verification of topological state in monolayer $\text{TaIrTe}_4$, but also
offers a strategy for the utilization of the new quantum topological states
based on switchable quantized responses.
