  Strategically combining four structured domains creates the first ever
three-way topological energy-splitter; remarkably, this is only possible using
a square, or rectangular, lattice, and not the graphene-like structures more
commonly used in valleytronics. To achieve this effect, the two mirror
symmetries, present within all fully-symmetric square structures, are broken;
this leads to two nondistinct interfaces upon which valley-Hall states reside.
These interfaces are related to each other via the time-reversal operator and
it is this subtlety that allows us to ignite the third outgoing lead. The
geometrical construction of our structured medium allows for the three-way
splitter to be adiabatically converted into a wave steerer around sharp bends.
Due to the tunability of the energies directionality by geometry, our results
have far-reaching implications for applications such as beam-splitters,
switches and filters across wave physics.
