Topological Phononic Logic.

Topological metamaterials have robust properties engineered from their macroscopic arrangement, rather than their microscopic constituency. They can be designed by starting from Dirac metamaterials with either symmetry-enforced or accidental degeneracy. The latter case provides greater flexibility in the design of topological switches, waveguides, and cloaking devices, because a large number of tuning parameters can be used to break the degeneracy and induce a topological phase. However, the design of a topological logic element-a switch that can be controlled by the output of a separate switch-remains elusive. Here we numerically demonstrate a topological logic gate for ultrasound by exploiting the large phase space of accidental degeneracies in a honeycomb lattice. We find that a degeneracy can be broken by six physical parameters, and we show how to tune these parameters to create a phononic switch that transitions between a topological waveguide and a trivial insulator by ultrasonic heating. Our design scheme is directly applicable to photonic crystals and may guide the design of future electronic topological transistors.