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.