  Employing the standard worldline-vortex mapping, we conclude that at the
critical temperature, superconductors demonstrate the magneto-halon effect with
respect to the quantized net magnetic flux generated by a solenoid inserted
into the system. The effect is a direct counterpart of the recently revealed
halon effect in terms of the quantized particle charge of a static impurity in
the two-dimensional U(1) quantum-critical environment. The flux-loop model
(a.k.a. frozen lattice superconductor) with a quasi-solenoid perturbation
proves to be the model of choice for qualitative and quantitative description
of both the halon and the magneto-halon effects.
