Glide-reflection symmetric phononic crystal interface: variation on a theme

Nodal points can be artificially synthesized using glide-reflection symmetries at crystal interfaces. This property was first demonstrated for a square-lattice phononic crystal at the X point of the first Brillouin zone (wavenumber k = +/- p/a with a the lattice constant), for a half-lattice-constant glide. Here we show that the nodal point can be moved to the Gamma point (k = 0) considering quarter-lattice-constant glide-reflection symmetry. Applying a continuous grading along the x-axis is further shown to leave the band structure mostly unaffected. In particular, the topological interface waves survive in the case that glide-reflection symmetry is only locally valid around the graded interface. As a result, the glide dislocation can be compensated for over a distance of a few crystal rows, to recover an apparently periodic crystal.

Automated summary

Nodal points can be synthesized at crystal interfaces using glide-reflection symmetries. In a square-lattice phononic crystal, the nodal point was previously observed at the X point, but in this study, it is shown that by considering quarter-lattice-constant glide-reflection symmetry, the nodal point can be moved to the Gamma point. Continuous grading along the x-axis does not significantly affect the band structure, allowing topological interface waves to survive even when glide-reflection symmetry is locally valid.