  Topological insulators, first observed in electronic systems, have inspired
many analogues in photonic and phononic crystals in which remarkable one-way
propagation edge states are supported by topologically nontrivial bandgaps.
Such bandgaps can be achieved by breaking the time-reversal symmetry to lift
the degeneracy associated with Dirac cones at the corners of the Brillouin
zone. Here, we report on our construction of a phononic crystal exhibiting a
Dirac-like cone in the Brillouin zone center. We demonstrate that
simultaneously breaking the time-reversal symmetry and altering the geometric
size of the unit cell result in a topological transition that is verified by
the Chern number calculation and edge mode analysis. The topology of the
bandgap is tunable by varying both the velocity field and the geometric size;
such tunability may dramatically enrich the design and use of acoustic
topological insulators.
