  Topological phase transition in a single material usually refers to
transitions between a trivial band insulator and a topological Dirac phase, but
the transition may also occur between different classes of topological Dirac
phases. However, it is a fundamental challenge to realize quantum transition
between Z2 nontrivial topological insulator (TI) and topological crystalline
insulator (TCI) in one material because Z2 TI and TCI are hardly both co-exist
in a single material due to their contradictory requirement on the number of
band inversions. The Z2 TIs must have an odd number of band inversions over all
the time-reversal invariant momenta, whereas, the newly discovered TCIs, as a
distinct class of the topological Dirac materials protected by the underlying
crystalline symmetry, owns an even number of band inversions. Here, take
PbSnTe2 alloy as an example, we show that at proper alloy composition the
atomic-ordering is an effective way to tune the symmetry of the alloy so that
we can electrically switch between TCI phase and Z2 TI phase when the alloy is
ordered from a random phase into a stable CuPt phase. Our results suggest that
atomic-ordering provides a new platform to switch between different topological
phases.
