Negative-μ regime in the ac magnetic response of superconductor nanoshells

► Vortices in superconducting spherical shells with nonuniform thickness are studied. ► The ac magnetic permeability μ of a 3D array of those shells is calculated. ► The real part of μ can be tuned from large positive to negative values. ► This tuning of μ can be realized by changing the applied dc magnetic field.