  Dual quantum spin Hall insulator (QSHI) is a newly discovered topological
state in the 2D material TaIrTe$_4$, exhibiting both a traditional $Z_2$ band
gap at charge neutrality point and a van Hove singularity (VHS) induced
correlated $Z_2$ band gap with weak doping. Inspired by the recent progress in
theoretical understanding and experimental measurements, we predicted a
promising dual QSHI in the counterpart material of the NbIrTe4 monolayer by
first-principles calculations. In addition to the well-known band inversion at
the charge neutrality point, two new band inversions were found after CDW phase
transition when the chemical potential is near the VHS, one direct and one
indirect $Z_2$ band gap. The VHS-induced non-trivial band gap is around 10 meV,
much larger than that from TaIrTe$_4$. Furthermore, since the new generated
band gap is mainly dominated by the $4d$ orbitals of Nb, electronic correlation
effects should be relatively stronger in NbIrTe$_4$ as compared to TaIrTe$_4$.
Therefore, the dual QSHI state in the NbIrTe$_4$ monolayer is expected to be a
good platform for investigating the interplay between topology and correlation
effects.
