  Novel materials with nontrivial electronic and photonic band topology are
crucial for realizing novel devices with low power consumption and heat
dissipation, and quantum computing free of decoherence. Here using
first-principles approach, we predict a class of ternary transition metal
chalcogenides (TTMC) MM'Te$_4$ exhibits dual topological characteristics:
quantum spin Hall (QSH) insulators in their 2D monolayers and topological Weyl
semimetals in their 3D noncentrosymmetric crystals upon van der Waals (vdW)
stacking. Remarkably, we find that one can create and annihilate Weyl fermions,
and realize the transition between Type-I and Type-II Weyl fermions by tuning
vdW interlayer spacing. Our calculations show that they possess excellent
thermodynamic stability and weak interlayer binding, implying their great
potentials for experimental synthesis, direct exfoliation and vdW
heterostacking. Moreover, their ternary nature will offer more tunability for
electronic structure by controlling different stoichiometry and valence
charges. Our findings provide an ideal materials platform for realizing QSH
effect and exploring topological phase transition, and will open up a variety
of new opportunities for two-dimensional materials and topological materials
research.
