  The possible existence of topological insulators in cubic pyrochlore iridates
A$_{2}$Ir$_{2}$O$_{7}$ (A = Y or rare-earth elements) is investigated by taking
into account the strong spin-orbit coupling and trigonal crystal field effect.
It is found that the trigonal crystal field effect, which is always present in
real systems, may destabilize the topological insulator proposed for the ideal
cubic crystal field, leading to a metallic ground state. Thus the trigonal
crystal field is an important control parameter for the metal-insulator
changeover. We propose that this could be one of the reasons why distinct low
temperature ground states may arise for the pyrochlore iridates with different
A-site ions. On the other hand, examining the electron-lattice coupling, we
find that softening of the $\textbf{q}$=0 modes corresponding to trigonal or
tetragonal distortions of the Ir pyrochlore lattice leads to the resurrection
of the strong topological insulator. Thus, in principle, a finite temperature
transition to a low-temperature topological insulator can occur via structural
changes. We also suggest that the application of the external pressure along
[111] or its equivalent directions would be the most efficient way of
generating strong topological insulators in pyrochlore iridates.
