  The discovery of new topological electronic materials brings a chance to
uncover novel physics and plays a key role in observing and controlling various
intriguing phenomena. 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 Tl$_2$Nb$_2$O$_{6+x}$ ($ 0\leq x \leq 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
Tl$_2$Nb$_2$O$_{6.5}$, leading to triply degenerate nodal points. When $x = 0$,
Tl$_2$Nb$_2$O$_6$ 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 $Tl^{1+}$ and
$Tl^{3+}$. This topological oxide will be promising for studying correlation
induced topological states and potential applications.
