Quantum spin Hall effect in monolayer and bilayer TaIrTe$_{4}$

Abstract: Generally, stacking two quantum spin Hall insulators gives rise to a trivial insulator. Here, based on first-principles electronic structure calculations, we confirm that monolayer TaIrTe${4}$ is a quantum spin Hall insulator and remarkably find that bilayer TaIrTe${4}$ is still a quantum spin Hall insulator. Theoretical analysis indicates that the covalent-like interlayer interaction in combination with the small bandgap at time-reversal invariant $\Gamma$ point results in new band inversion in bilayer TaIrTe${4}$, namely, the emergence of quantum spin Hall phase. Meanwhile, a topological phase transition can be observed by increasing the interlayer distance in bilayer TaIrTe${4}$. Considering that bulk TaIrTe${4}$ is a type-II Weyl semimetal, layered TaIrTe${4}$ thus provides an ideal platform to realize different topological phases at different dimensions.