Switchable quantized signal between longitudinal conductance and Hall conductance in dual quantum spin Hall insulator TaIrTe$_4$

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.