Magnetic detectability of a finite size paramagnet/superconductor cylindrical cloak

Cloaking of static magnetic fields by a finite thickness type-II superconductor tube surrounded by a coaxial paramagnet shell is studied. On the basis of exact solutions to the London and Maxwell equations, it is shown that perfect cloaking is realizable for arbitrary geometrical parameters including the thin film case for both constituents. In contrast to previous approximate studies assuming perfect diamagnetism of the superconductor constituent, it is proven that cloaking provides simultaneously full undetectability, that is the magnetic moment of the structure completely vanishes as well as all high-order multipole moments as soon as the uniform field outside remains unaffected.