Topological phases in pyrochlore thallium niobate Tl₂Nb₂O_6+x

The discovery of new topological electronic materials brings a chance to uncover new physics. Up to now, many materials have been theoretically proposed and experimentally proved to host different kinds of topological states. Unfortunately, there is little convincing experimental evidence for the existence of topological oxides. The reason is that oxidation of oxygen leads to ionic crystal in general and makes band inversion unlikely. In addition, the realization of different topological states in a single material is quite difficult, but strongly needed for exploring topological phase transitions. In this work, using first-principles calculations and symmetry analysis, we propose that the experimentally tunable continuous solid solution of oxygen in pyrochlore Tl₂Nb₂O_6+x (0 ≤ x ≤ 1.0) leads to various topological states. Topological insulator, Dirac semimetal, and triply degenerate nodal point semimetal can be realized in it via changing the oxygen content and/or tuning the crystalline symmetries. When x = 1, it is a semimetal with quadratic band touching point at Fermi level. It transits into a Dirac semimetal or a topological insulator depending on the in-plane strain. When x = 0.5, the inversion symmetry is spontaneously broken in Tl₂Nb₂O_6.5, leading to triply degenerate nodal points. When x = 0, Tl₂Nb₂O₆ becomes a trivial insulator with a narrow band gap. These topological phase transitions driven by solid solution of oxygen are unique and physically plausible due to the variation of valence state of Tl⁺ and Tl³⁺. This topological oxide will be promising for studying correlation induced topological states and potential applications.