AbstractThe study on quantum spin Hall effect and topological insulators formed the prologue to the surge of research activities in topological materials in the past decade. Compared to intricately engineered quantum wells, three-dimensional weak topological insulators provide a natural route to the quantum spin Hall effect, due to the adiabatic connection between them and a stack of quantum spin Hall insulators, and the convenience in exfoliation of samples associated with their van der Waals-type structure. Despite these advantages, both theoretical prediction and experimental identification of weak topological insulators remain scarce. Here, based on first-principles calculations, we show that AuTe₂Br locates at the boundary between a strong and a weak topological semimetal state. We identify the key structural parameter that dictates the traversal of the topological transition, which can be easily realized in experiments. More interestingly, the critical topology of AuTe₂Br persists up to an applied pressure of ~15.4 GPa before a structural phase transition accompanied by a change of electronic topology and the onset of superconductivity. Our results establish AuTe₂Br as a new candidate for an effective tuning between weak and strong topological phases in a single material, with the potential to realize various other topological phases of matter.