Acoustic computing: At tunable pseudospin-1 Hermitian Dirac-like cone.

Hermitian Dirac-like cones are proposed for creating acoustic logic gates herein. The predictive phenomenon of creating Dirac-like cones near a bipolar antisymmetric deaf band was found to be useful for acoustic computing of Boolean algebra. Unlike previous approaches, Dirac-like cone creates exclusive opportunity to perform all possible Boolean algebra computation with valid inputs. The phenomenon is demonstrated in two-dimensional phononic crystals (PnCs), consisting of tunable square columns in air media. By predictive tuning of the deaf bands, a triply to doubly degenerated Dirac-like cone is reported to form and is particularly useful for acoustic computing. It is only possible when a bottom band has a negative curvature that is lifted from a nearby doubly degenerated band with positive curvature, which is again degenerated with a deaf band. On the contrary, similar computing possibilities are difficult when the bottom band degenerates with the deaf band and the top band is lifted. Using these phenomena, acoustic logic gates are designed to perform Boolean algebra through AND, NAND, OR, and NOR gate operations. A simple one degree of freedom system and a complex six degrees of freedom system are proposed and demonstrated in which simple rotation of the PnCs activates a specific gate.