Fig. 1

Hermitian concentric square crystal. a Schematic representation of the crystal made of 8a × 8a metamolecule arrays defining the non-trivial region with D/a = 0.714 enclosed by a trivial region with D/a = 0.280 and thickness 5a. Circles represent the position of the source exciting the bulk (black), the edge (green) and the corner states (red), which correspondingly are indicated by stars. b Comparison between the real eigenfrequencies obtained by finite element method simulations (dots) with the normalized pressure of the excited states from the multiple scattering theory computation. c Pressure maps of all corner states. Inserts illustrate the excitation point