  In recent years, the confinement of light in open systems with no radiation
leakage has raised great interest in the scientific community, both due to its
peculiar and intriguing physics and due to its important technological
applications. In particular, materials with near-zero permittivity offer a
unique opportunity for light localization, as they enable the formation of
embedded eigenstates in core-shell systems with suppressed radiation loss. For
all the solutions presented thus far in the literature, the exact suppression
of the radiation leakage can occur only when the size of the resonator is
delicately tuned. Surprisingly, here it is shown that the tuning of the
resonator radius may be unnecessary, and that nonlocal metal spherical
nanostructures of any size may support multiple embedded eigenstates with a
monopole-type symmetry.
