Double Dirac cone in two-dimensional phononic crystals beyond circular cells

Abstract

A double Dirac cone plays a significant role in the design of zero-refractive-index metamaterials without phase variation and topological insulators with pseudospin states. We present a study on the formation of a double Dirac cone in two-dimensional phononic crystals consisting of either hexagonal or triangular columns in air. We arranged hexagonal and triangular columns separately in a honeycomb lattice to explore the influence of phononic crystal symmetry on the formation of the double Dirac cone. The results show that phononic crystals forming a honeycomb lattice with C6v or C6 symmetry induce an accidental degeneracy, but C3v and C3 cannot. We also demonstrate that by varying the filling ratio of the hexagonal columns, a topological phase transformation induced by energy band inversion with dipolar and quadrupolar states occurs near the double Dirac cone. Transmission properties for acoustic tunneling and waveform shaping are confirmed in two numerical simulation examples. A discussion is given on the formation of the double Dirac cone in different phononic crystal symmetries in a honeycomb lattice. The conclusions suggest a new route for designing topological and zero-refractive-index acoustic devices.