Universal route for the emergence of exceptional points in PT-symmetric metamaterials with unfolding spectral symmetries

We introduce a class of parity-time symmetric elastodynamic metamaterials (Ed-MetaMater) whose Hermitian counterpart exhibits unfolding (fractal) spectral symmetries. Our study reveals a scale-free formation of exceptional points in those Ed-MetaMaters whose density is dictated by the fractal dimension of their Hermitian spectra. We demonstrate this scale-free EP-formation in a quasi-periodic Aubry-Harper Ed-MetaMater, a geometric H-tree-fractal Ed-MetaMater, and an aperiodic Fibonacci Ed-MetaMater—each having a specific fractal spectrum—using finite element models and establish a universal route for EP-formation via a coupled mode theory model with controllable fractal spectrum. This universality may enable the rational design of novel Ed-MetaMater for hypersensitive sensing and elastic wave control.