Transition between strong and weak topological insulator in ZrTe₅ and HfTe₅

ZrTe₅ and HfTe₅ have attracted increasingly attention recently since the theoretical prediction of being topological insulators (TIs). However, subsequent works show many contradictions about their topolog-ical nature. Three possible phases, i.e. strong TI, weak TI, and Dirac semi-metal, have been observed in different experiments until now. Essentially whether ZrTe₅ or HfTe₅ has a band gap or not is still a question. Here, we present detailed first-principles calculations on the electronic and topological prop-erties of ZrTe₅ and HfTe₅ on variant volumes and clearly demonstrate the topological phase transition from a strong TI, going through an intermediate Dirac semi-metal state, then to a weak TI when the crystal expands. Our work might give a unified explain about the divergent experimental results and propose the crucial clue to further experiments to elucidate the topological nature of these materials.