  We investigate interference between topological interfacial modes in a
semiconductor photonic crystal platform with Dirac frequency dispersions, which
can be exploited for interferometry switch. It is showcased that, in a
two-in/two-out structure with four topological waveguides, geometric phases of
the two-component spinor wavefunctions of topological photonic modes accumulate
at turning points of waveguides, which govern the interferences and split the
electromagnetic energy into two output ports with relative power ratio tunable
by the relative phase of inputs. We unveil that this brand-new photonic
phenomenon is intimately related to the spin-momentum locking property of
quantum spin Hall effect, and results from the symphonic contributions of three
phase variables: the spinor phase and geometric phase upon design, and the
global phase controlled from outside. The present findings open the door for
manipulating topological interfacial modes, thus exposing a new facet of
topological physics. The topology-driven interference can be incorporated into
other devices which is expected to leave far-reaching impacts to advanced
photonics, optomechanics and phononics applications.
